Synthetic Division

Key Questions

• How can synthetic division be used to factor a polynomial?

  Here is a reasonable Pre-Calculus example of synthetic division to illustrate the concept.

  Let's say you had:

  #2x^4 - 3x^3 - 5x^2 + 3x + 8#

  Like Joan said, there is a trial and error aspect to this.

  Look at all the coefficients, and think about what a common factor might be.

  • If you don't get a zero remainder, then the factor doesn't really work and you should try again.
  • If the possible factors are all used up, maybe it isn't factorable.

  Here, factors you might try include the ones that correspond to the fourth order coefficient (#2#) and the zeroth order coefficient (#8#).

  • #8# has factors of #1, 2, 4#, and #8#.
  • #2# has factors of #1# and #2#.

  So the possible factors might be said to be #pmp/q#, where #p# consists of the factors of the zeroth degree coefficient, and #q# consists of the factors of the highest degree coefficient.

  You can therefore have factors of:

  #pm[1, 2, 4, 8, 1/2]#

  So you can try all of these (#2/2#, #4/2#, and #8/2# are duplicates). Recall that if #-a# is used as what is written in the synthetic division process on the left corner, it corresponds to #x+a#.

  We will use #-1# here. I tend to try #1# and #-1# first, and go up in value, and try the fractions last.

  #ul(-1|)" "2" "-3" "-5" "" "3" "" "8#

  Drop down the #2#, and multiply by the #-1# to get #-2#.

  #ul(-1 |)" "2" "-3" "-5" "" "3" "" "8#
  #ul(" "" "" "" "-2" "" "" "" "" "" "" "" ")#
  #" "" "color(white)(.)2#

  Add #-3# and #-2#, then multiply the resultant #-5# by #-1# again.

  #ul(-1 |)" "2" "-3" "-5" "" "3" "" "8#
  #ul(" "" "" "" "-2" "" "5" "" "" "" "" "" ")#
  #" "" "color(white)(.)2" "-5#

  Repeat until you're done.

  Add #-3# and #-2#, then multiply the resultant #-1# by #-1# again.

  #ul(-1 |)" "2" "-3" "-5" "" "3" "" "8#
  #ul(" "" "" "" "-2" "" "5" "color(white)(.)" "0color(white)(.)" "-3" ")#
  #" "" "color(white)(.)2" "-5" "" "0" "" "3" "" "5#

  Your answer here happens to be this, where 2 corresponds to #2x^3#, since you divided a fourth-order polynomial by a first-order polynomial.

  So, one way to express the result is:

  #(2x^4 - 3x^3 - 5x^2 + 3x + 8)/(x+1)#

  #= color(blue)(overbrace(2x^3 - 5x^2 + 0x + 3)^"Quotient Term" + overbrace(5/(x+1))^"Remainder Term")#

  where the #5/(x+1)# was written by saying that the last value below the horizontal bar (below #-2, 5, 0, -3#), being #5#, is divided by the #x pm a# equation such that #x pm a = 0#. So, #x+1# indicates that the factor we have just used is #-1#.

  (Naturally, if the remainder is #0#, you do not have the remainder fraction at the end.)

  Truong-Son N. · 4 · Apr 11 2015
• How do you write the remainder in synthetic division?

  The remainder in synthetic division could be written as a fraction or with R written in front of it. If writing as a fraction, the remainder is in the numerator of the fraction and the divisor is in the denominator.

  For example:

  Dividing #x^2 + 3x - 12 # by #x - 3#:

  When you use Synthetic Division, the answer is #x + 6# with a remainder of 6.
  Here are two ways you can write the answer:

  1. x + 6 R 6

  2. #x + 6 + 6/(x - 3)#

  Elizabeth P. · · Oct 6 2014
• How do I find the roots of a polynomial function by using synthetic division?

  Please see the video below for a detail explanation.

  Synthetic Divisioin Roots

  AJ Speller · · Sep 13 2014
• What is synthetic division?

  Answer:

  Synthetic division is a way to divide a polynomial by a linear expression.

  Explanation:

  Suppose our problem is this: #y=x^3+2x^2+3x-6#

  Now, the main use of synthetic division is to find the roots or solutions to an equation.

  The process for this serves to cut down on the gessing you have to do to find a value of x that makes the equation equal 0.

  First, list the possible rational roots, by listing the factors of the constant (6) over the list of the factors of the lead coefficient (1).

  #+-#(1,2,3,6)/1

  Now, you can begin trying numbers. First, you simplify the equation to just the coefficients:
  )¯¯1¯¯¯2¯¯¯¯3¯¯¯¯-6¯¯

  And now, plug your possible rational roots in, one at a time, until one works. (I suggest doing 1 and -1 first, since they're the easiest)

  1 )¯¯1¯¯¯2¯¯¯¯3¯¯¯¯-6¯¯

  #color(white)¯¯#¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

  1 .First bring down the lead number (1)

  1 )¯¯1¯¯¯2¯¯¯¯3¯¯¯¯-6¯¯

  #color(white)¯¯#¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  #color(white)00#1

  2 . Now multiply that number by the divisor (1)

  1 )¯¯1¯¯¯2¯¯¯¯3¯¯¯¯-6¯¯

  #color(white)¯¯#¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  #color(white)00#1

  3 . Now place the product underneath the second number (2)

  1 )¯¯1¯¯¯2¯¯¯¯3¯¯¯¯-6¯¯
  #color(white)ddots##color(white)00#1
  #color(white)¯¯#¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  #color(white)00#1#color(white)00#

  4 . Now add the two numbers together (2&1) and move the sum down

  1 )¯¯1¯¯¯2¯¯¯¯3¯¯¯¯-6¯¯
  #color(white)ddots##color(white)00#1
  #color(white)¯¯#¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  #color(white)sum#1#color(white)00#3

  5 . Now multiply the sum (3) by the divisor (1) and move it underneath the next value in the dividend

  1 )¯¯1¯¯¯2¯¯¯3¯¯-6¯¯
  #color(white)ddots##color(white)00#1#color(white)00#3
  #color(white)¯¯#¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  #color(white)sum#1#color(white)00#3

  6 . Now add the two values together (3&3) and move the sum down

  1 )¯¯1¯¯¯2¯¯¯3¯¯-6¯¯
  #color(white)ddots##color(white)00#1#color(white)00#3
  #color(white)¯¯#¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  #color(white)sum#1#color(white)00#3#color(white)00#6

  7 . Now multiply the new sum (6) with the divisor (1) and move it underneath the next value in the dividend

  1 )¯¯1¯¯¯2¯¯¯3¯¯-6¯¯
  #color(white)ddots##color(white)00#1#color(white)00#3#color(white)00#6
  #color(white)¯¯#¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  #color(white)sum#1#color(white)00#3#color(white)00#6

  8 . Now add together the two values (6&-6) and move that sum down

  1 )¯¯1¯¯¯2¯¯¯3¯¯-6¯¯
  #color(white)ddots##color(white)00#1#color(white)00#3#color(white)00#6
  #color(white)¯¯#¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  #color(white)sum#1#color(white)00#3#color(white)00#6#color(white)00#0

  8 . Now you have the equation, 0=#x^2+3x+6#, with the sums you found being the coeffiecients

  1 )¯¯1¯¯¯2¯¯¯3¯¯-6¯¯
  #color(white)ddots##color(white)00#1#color(white)00#3#color(white)00#6
  #color(white)¯¯#¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
  #color(white)sum#1#color(white)00#3#color(white)00#6#color(white)00#0

  Rachel · 2 · Jan 14 2016

• What is synthetic division?
• What are common mistakes students make with synthetic division?
• How do I find the quotient and remainder using synthetic division?
• How do you write the remainder in synthetic division?
• How do I find the quotient #(x^3+5x^2+x-15)/(x+3)# by using synthetic division?
• How do I find the roots of a polynomial function by using synthetic division?
• How can synthetic division be used to factor a polynomial?
• How do I use synthetic division to find #p(-3)# for #p(x)=x^4-2x^3-4x+4#?
• Use synthetic division to find #p(4)# for #p(x)=x^4-2x^3-4x+4#?
• How do you use synthetic division to evaluate #f(3)# given that #f(x)=x^3+2x^2-7x+8#?
• How do you list all possible rational roots for each equation, use synthetic division to find the actual rational root, then find the remaining 2 roots for #x^3-2x^2+9x-18=0#?
• How do you list all possible rational roots for each equation, use synthetic division to find the actual rational root, then find the remaining 2 roots for #2x^3-7x^2-46x-21=0#?
• How do you use synthetic substitution to evaluate the polynomial #p(x)=x^3-4x^2+4x-5# for x=4?
• How do you use synthetic substitution to find f(-2) for #f(x)=x^4-4x^3-4x+6#?
• How do you use synthetic substitution to find x=2 for #f(x) = 3x^5-2x^2+x#?
• How do you use synthetic substitution to find x=-3 for #f(x) = 2x^2-4x+7#?
• How do you use synthetic substitution to find #f(x)# for x=2 given #f(x)=7x^4-3x^3+x^2+5x-9#?
• How do you use synthetic substitution to find x=-3 for #g(x)=x^3-8x+6#?
• How do you use synthetic substitution to find the real zeroes for #P(x)=x^4-6x^3+11x^2-8x+2#?
• How do you use synthetic substitution to find x=-3 for # f(x)= -x^4+x^3-x+1#?
• How do you use synthetic substitution to find x=2 for #f(x)= 3x^5-2x^2+x#?
• How do you use synthetic substitution to find f(1+i) for #f(x)=-x^3+2x^2+3x-5#?
• How do you use synthetic substitution to find f(-2) for #f(x) = x^4 - 4x^3 - 4x + 6 #?
• How do you use synthetic substitution to find g(-5) and g(4) for #g(x)= 9x^4 - 8x^2 + 9x - 5#?
• How do you use synthetic substitution to find f(3) and f(-4) for #f(x)= x^4-8x-11#?
• How do you use synthetic substitution to find p(-4) for #p(x)=3x^3-2x^2+6x-4#?
• How do you use synthetic substitution to find p(-3) for #p(x)=4x^3-5x^2+7x-10#?
• How do you use synthetic substitution to find f(-2) for #f(x) = x^4 - 4x^3 - 4x + 6#?
• How do you use synthetic substitution to find f(3) for # f(x) = 2x^4 - 3x^2 - x + 2#?
• How do you use synthetic substitution to find x=-5 for #P(x) = x^3 + 4x^2 - 8x - 6#?
• How do you use synthetic substitution to find P(2) for # P(x) = 4x^3 - 5x^2 + 7x - 9#?
• How do you use synthetic substitution to find x=3 for #f(x)=-3x^3+7x^2-4x+8#?
• How do you use synthetic substitution to find x=4 for #p(x)=x^3-4x^2+4x-5#?
• How do you use synthetic substitution to factor #x^3+9x^2+24x+20# if x+5 is one of its factor?
• How do you use synthetic substitution to evaluate x=4 for #P(x)= x^3 - 4x^2 + 4x - 5#?
• How do you use synthetic substitution to evaluate f(-3) for #f(x)=2x^3-6x^2-5x+7#?
• How do you use synthetic substitution to evaluate f(-2) for #f(x)=x^4-4x^3-4x+6#?
• How do you use synthetic substitution to evaluate P(3) for # P(x) = 2x^3 - 3x^2 - 5x - 1#?
• How do you use synthetic substitution to evaluate f(2) for #f(x)=x^3+2x^2-4x-5#?
• How do you use synthetic substitution to evaluate f(2) for #f(x)=x^4-4x^3+2x^2-3#?
• How do you use synthetic substitution to evaluate f(-3) for #f(x)=x^4-4x^3+2x^2-4x+6#?
• How do you use synthetic substitution to evaluate f(-2) for #f(x)=x^3-3x^2-x-9#?
• How do you use synthetic substitution to find f(3) and f(-2) for # f(x)=x^2-4x+4#?
• How do you use synthetic substitution to find f(3) and f(-2) for #f(x)=x^4-5x+2#?
• How do you use synthetic substitution to find f(3) and f(-2) for #f(x)=x^2-5#?
• How do you use synthetic substitution to find x=1 for #P(x)=4x^3-5x^2+3#?
• How do you use synthetic division to divide #x^4+4x^3+6x^2+4x+1# by #x+1#?
• How do you use synthetic division to find x=-1 for #P(x)= x^3+2x^2-5x+6 #?
• How do you use synthetic division to find x=2 for #P(x) = x^4+x^2+x-6#?
• How do you use synthetic division to find f(-3) for #f(x)=x^4-4x^3+2x^2-4x+6#?
• How do you divide using synthetic division: #(2x^3 - 4x^2 - 7x + 5)/(x - 3)#?
• How do you divide using synthetic division: #(2u^4 - 5u^3 - 12u^2 + 2u - 8)/(u - 4)#?
• How do you divide using synthetic division: #(y^4 - 4y^2 + y + 4)/(y + 2)#?
• How do you use synthetic division to divide# (x^2+4x+1)# by #x-5#?
• How do you use synthetic division to divide#(x^2-8x+6)# by #x+2#?
• How do you use synthetic division to divide #3x^3 - x^2 + 8x-10# by #x-1#?
• How do you use synthetic division to find #f(sqrt{3})# if #f(x)=2x^3-6x+5#?
• How do you use synthetic division to find all the rational zeroes of the function #f(x)= 2x^3 - 3x^2-11x+6#?
• How do you use synthetic division to find factors for #x^3 + 2x^2 - 5x - 6#?
• How do you use synthetic division to divide #x^3+8x^2-3x+16# by #(x^2 + 5)#?
• How do you use synthetic division to divide #x^3+5x^2-x-9# by #x+2#?
• How do you use synthetic division to divide #(6t^3+5t^2+9)# by #2t+3#?
• How do you use synthetic division to divide #(14x^2 - 34)# by #x+4#?
• How do you use synthetic division and Remainder Theorem to find P(a) if #P(x) = x^3 - 8x^2 + 5x - 7# and a = 1?
• How do you use synthetic division to divide #(x^3 -8 x^2 - 25x + 203)# by #x-5#?
• How do you use synthetic division to find the factors of #x^3 - 3x^2 - 10x + 24#?
• How do you use synthetic division to divide #6n^4-33n^3+16n^2+5n-55# by #n-5#?
• How do you use synthetic division to divide #12x^3 -19x -12# by #2x-3#?
• How do you use synthetic division to divide #x^4-3x^3+3x^2-2x+3# by #x^2-3x+2#?
• How do you use synthetic division to divide #x^3+5x^2+x-15# by #x+3#?
• How do you use synthetic division to divide #3x^5+4x^4+2x^2-1# by #x+2#?
• How do you use synthetic division to divide #(12x^4 + 20x^3 - 24x^2 + 20x + 35) # by #3x+5#?
• How do you use synthetic division to divide #(4x^2 - 2x + 6)# by #2x-3#?
• How do you use synthetic division to divide #12x^3 + 19x^2 - 13x - 6# by #2x-1#?
• How do you use synthetic division to divide #(x^2 + 13x + 40) ÷ (x + 8)#?
• How do you use synthetic division to divide #(2x^2 – 23x + 63) ÷ (x – 7)#?
• How do you use synthetic division to divide #4x^3 + 7x^2 – 13x – 3# by #x + 3#?
• How do you use synthetic division to divide #x^4 – 8x^3 + 16x^2 – 19# by #x-5#?
• How do you use synthetic division to divide #(x^4-11x^3+15x^2+40x-5)# by #x-5#?
• How do you use synthetic division to find if x+1 is a factor for #f(x)=2x^3+5x^2-x-4#?
• How do you use synthetic division to see if -1 is a zero of #h(x)=x^4+9x^3+18x-8#?
• How do you use synthetic division to divide #(x^2 + 13x + 40) ÷ (x + 8)#?
• How do you use synthetic division to divide #(2x^2 – 23x + 63) ÷ (x – 7) #?
• How do you use synthetic division to divide #4x^3 + 7x^2 – 13x – 3# by #x-7#?
• How do you use synthetic division to divide #3x^3 – 4x – 1 # by #x+1#?
• How do you use synthetic division to divide #x^4 – 8x^3 + 16x^2 – 19# by #x-5#?
• How do you use synthetic division to divide #3x^3 - x^2 + 8x-10# by #x-1#?
• How do you use a graph, synthetic division, and factoring to find all the roots of an equation #x^3 + 5x^2 + 3x -9 = 0#?
• How do you use synthetic division to divide #3x^3+4x^2-7x+1# by #3x-2#?
• How do you use synthetic division to divide #(2x^3 + x^2 - 2x + 2) # by #x+2#?
• How do you use synthetic division to divide #x^3- 6x^2+ 11x - 6 # by #x-1#?
• How do you use synthetic division to find P(4) for #P(x)= x^4 + x^3 + 10x^2 + 9x - 6#?
• How do you use synthetic division to divide #3x^3 + 2x^2 + 6x - 2# by #x+2#?
• How do you use synthetic division to divide #4a^2 + 19a + 21# by #a+1#?
• How do you use synthetic division to divide #x^3 - 5x^2 + 2x + 8# by #x-2#?
• How do you use synthetic division to divide #y^2 + 25# by #y+5#?
• How do you use synthetic division to divide #x^3 + 2x^2 - 2x + 24# by #x+4#?
• How do you divide #2x^3 + 6x^2 - 2x - 5# by #x + 3# using synthetic division?
• How do you use synthetic division to find the factors of #f(x)= x^4 -x^3 -19x^2+49x-30#?
• How do you use synthetic division to find the zeroes of #f(x)= x^4 -3x^3-9x^2-3x-10#?
• How do you use synthetic division to find the x intercepts of #g(x)=x^3 -3x +2#?
• How do you use synthetic division to divide #(4x^2 - 2x + 6) (2x - 3) ^ -1#?
• How do you use synthetic division to divide #(2x^3-x^2+5x-12) /(2x - 3) #?
• How do you use synthetic division to divide #(x^4 + 2x^3 - 2x - 1) ÷ (x^3 + 3x^2 + 3x + 1)#?
• How do you use synthetic division to divide #(x^3-2x-22x+40)# divided by (x-4)?
• How do you use synthetic division to find: f(-2): #f(x) = 3x^4 - 2x^2 + 1#?
• How do you use synthetic division to factor #x^4 + 4x^3 - 7x^2 - 34x -24#?
• How do you use synthetic division to divide #y= x^3 + 3x^2 - 13x - 15# , (x + 5)?
• How do you use synthetic division to divide #x^3-2x^2+2x-5# divided by (x-1)?
• How do you use synthetic division to divide #x^4-4x^2+7x+15# divided by x+4?
• How do you use synthetic division to #f(x)=x^5-x^4+x^3-x+5#; find f(1+i)?
• How do you use synthetic division to divide #16x^3+8x^2-40x-115# divided by #2x-5#?
• How do you use synthetic division to divide #2x^3-3x^2-5x-12div x-3#?
• How do you use synthetic division to divide #(x^4 – 16) ÷ (x + 2)#?
• How do you use synthetic division to divide #X^3 + 2x^2 - 5x - 6 div (x + 3)#?
• How do you use synthetic division to divide #( 6x^3 - x^2 - 7x + 5 ) / ( x - 3 )#?
• How do you use synthetic division to divide #( x^4 + 3x^3 - 5x^2 + 9 ) / ( x + 3 )#?
• How do you use synthetic division to divide #( x^4 + 3x^3 - 5x^2 + 9 ) / ( x + 4 )#?
• How do you use synthetic division to divide #( x^4 - 2x^3 + x - 8 ) / ( x - 1 )#?
• How do you use synthetic division to divide #( 4x^4 - 2x^2 - 1 ) / ( 2x - 1 )#?
• How do you use synthetic division to divide #( 2x^3 + 3x^2 + 4 ) / ( 2x + 1 )#?
• How do you use synthetic division to divide #( 6x^3 - 9x^2 - 12x - 6 ) / ( 3x + 4 )#?
• How do you use synthetic division to divide #(14x^2 - 34) / (x + 4)#?
• How do you use synthetic division to divide #(-14x^3-13x^2-11) / (2x+3)#?
• Question #e7b5e
• How do you use synthetic division to divide #(x^7 - x^6 + x^5 - x^4 + 2) / (x + 1)#?
• How do you use synthetic division to divide #(2x^4 + 3x^2 - 1) / (x - 1/2)#?
• How do you use polynomial division to determine whether x=3 is a root of #x^3+x^2+15-x#?
• How do you use polynomial division to divide #x^3 + x^2 - 10x - 6# by x-3?
• How do you use synthetic division to divide #5x^77 - 4x^60 + 2x^43 + 6x^30 - 4x^19 + 2# divided by x - 1?
• How do you divide #(3x^2 - 8x + 4) -: (x-2)# by synthetic division?
• What Is the quotient of #(x^3 + 6x^2 + 11x + 6) -: (x^2 + 4x + 3)#?
• What is the remainder when #(x^4 + 36)# is divided by #(x^2 - 8)#?
• How do you express #0.0001/0.04020# as a decimal?
• How do you graph #f(x)=5x^3-7x^2-49x+51# on a calculator, use the graph to guess the possible linear factors of f(x). then completely factor f(x) with the aid of synthetic division?
• How do you find all rational zeroes of the function using synthetic division #f(x)=x^3-7x^2+2x+40#?
• How do you find all rational zeroes of the function using synthetic division #f(x)=x^4+x^3+x^2-9x-10#?
• How do you find all rational zeroes of the function using synthetic division #f(x)=3x^3+12x^2+3x-18#?
• How do you find all rational zeroes of the function using synthetic division #f(x)=2x^5+x^4-23x-16#?
• How do you divide #3x^3-4x^2-17x+6# by 3x-1 and is it a factor of the polynomial?
• How do you divide #y^4-8y^3+10y^2+2y+4# by y-2 and is it a factor of the polynomial?
• How do you divide #4v^3+6v^2-8v-12# by 2v-3 and is it a factor of the polynomial?
• How do you completely factor #x^3+9x^2+12x+15# given x+5 is one of the factors?
• How do you completely factor #x^3-x^2-14x+25# given x-3 is one of the factors?
• How do you completely factor #25x^3+150x^2+131x+30# given 5x+3 is one of the factors?
• How do you completely factor #6x^3+7x^2-1# given #2x+1# is one of the factors?
• How do you list all possible roots and find all factors of #x^5+7x^3-3x-12#?
• How do you list all possible roots and find all factors of #6x^3+7x^2-3x-1#?
• How do you list all possible roots and find all factors of #x^4+2x^3-8x^2+16x-23#?
• How do you list all possible roots and find all factors of #3x^2+2x+2#?
• How do you list all possible roots and find all factors of #x^3+27#?
• How do you list all possible roots and find all factors of #4x^2-9#?
• How do you list all possible roots and find all factors and zeroes of #x^3+4x^2+5x+2#?
• How do you list all possible roots and find all factors and zeroes of #5x^3+29x^2+19x-5#?
• How do you list all possible roots and find all factors and zeroes of #x^4-x^3+14x^2-16x-32#?
• How do you list all possible roots and find all factors and zeroes of #4x^3-9x^2+6x-1#?
• How do you list all possible roots and find all factors and zeroes of #3x^4-10x^3-24x^2-6x+5#?
• How do you list all possible roots and find all factors and zeroes of #3x^3+9x^2+4x+12#?
• How do you divide #24x^4+31^3+7x^2+4x+10# by #3x+2#?
• How do you use synthetic division on #-2x^4+14x^2+6# and find p(-3)?
• How do you evaluate #f(x)=2x^3+5x^2+4x+8# at x=-2 using direct substitution and synthetic division?
• How do you evaluate #f(x)=2x^3-x^4+5x^2-x# at x=3 using direct substitution and synthetic division?
• How do you evaluate #f(x)=x+1/2x^3# at x=4 using direct substitution and synthetic division?
• How do you evaluate #f(x)=5x^4-8x^3+7x^2# at x=1 using direct substitution and synthetic division?
• How do you evaluate #f(x)=x^3+3x^2-2x+5# at x=-3 using direct substitution and synthetic division?
• How do you evaluate #f(x)=11x^3-6x^2+2# at x=0 using direct substitution and synthetic division?
• How do you evaluate #f(x)=7x^3+9x^2+3x# at x=10 using direct substitution and synthetic division?
• How do you evaluate #f(x)=-x^5-4x^3+6x^2-x# at x=-2 using direct substitution and synthetic division?
• How do you evaluate #f(x)=5x^3+4x^2+8x+1# at x=2 using direct substitution and synthetic division?
• How do you evaluate #f(x)=-3x^3+7x^2-4x+8# at x=3 using direct substitution and synthetic division?
• How do you evaluate #f(x)=x^3+3x^2+6x-11# at x=-5 using direct substitution and synthetic division?
• How do you evaluate #f(x)=-4x^3+3x-5# at x=2 using direct substitution and synthetic division?
• How do you evaluate #f(x)=-x^4+x^3-x+1# at x=-3 using direct substitution and synthetic division?
• How do you evaluate #f(x)=2x^4+x^3-3x^2+5x# at x=-1 using direct substitution and synthetic division?
• How do you evaluate #f(x)=3x^5-2x^2+x# at x=2 using direct substitution and synthetic division?
• How do you evaluate #f(x)=-x^4+8x^3+13x-4# at x=-2 using direct substitution and synthetic division?
• How do you divide #(r^3+6r^2-21r-18) div (r-3)# using synthetic division?
• How do you divide #(x^3-11x^2+22x+40)div(x-5)# using synthetic division?
• How do you divide #(9x^3-19x^2-28x+12)div(x-3)# using synthetic division?
• How do you divide #(m^3-13m^2+24m+18)div(m-3)# using synthetic division?
• How do you divide #(x^3+15x^2+45x-25)div(x+5)# using synthetic division?
• How do you divide #(a^3+5a^2+14a+16)div(a+2)# using synthetic division?
• How do you divide #(2x^3+9x^2+2x-21)div(x+3)# using synthetic division?
• How do you divide #(10r^3-22r^2-17r-21)div(r-3)# using synthetic division?
• How do you divide #(n^3+6n^2+4n-2)div(n+1)# using synthetic division?
• How do you divide #(7m^3+16m^2-7m+27)div(m+3)# using synthetic division?
• How do you divide #(5x^3-2x^2+5x-16)div(x-1)# using synthetic division?
• How do you divide #(b^3+2b^2-15b+49)div(b+6)# using synthetic division?
• How do you divide #(3x^2+7x+2)div(x+2)# using synthetic division?
• How do you divide #(2x^2+7x-15)div(x+5)# using synthetic division?
• How do you divide #(4x^2+x+1)div(x-2)# using synthetic division?
• How do you divide #(3x^2+4x-x^4-2x^3-4)div(x+2)# using synthetic division?
• How do you divide #(3x^2-4+x^3)div(x-1)# using synthetic division?
• How do you divide #(x^4+1)div(x+1)# using synthetic division?
• How do you divide #(x^4+9)div(x+3)# using synthetic division?
• How do you divide #(x^4-16)div(x+2)# using synthetic division?
• How do you divide #(x^6+4x^5-2x^3+7)div(x+1)# using synthetic division?
• How do you divide #(n^3+n^2-11n+18)div(n-1)# using synthetic division?
• How do you divide #(m^3+6m^2+9m-5)div(m+1)# using synthetic division?
• How do you divide #(x^3-6x^2-6x+9)div(x+1)# using synthetic division?
• How do you divide #(3r^3+34r^2+89r+75)div(r+8)# using synthetic division?
• How do you divide #(6b^3+28b^2+25b-21)div(b+3)# using synthetic division?
• How do you divide #(8r^3-55r^2+44r-12)div(r-6)# using synthetic division?
• How do you divide #(n^3-9n-3)div(n+3)# using synthetic division?
• How do you divide #(2x^3+28x^2+86x+60)div(x+10)# using synthetic division?
• How do you divide #(m^3-2m^2-11m-6)div(m+2)# using synthetic division?
• How do you divide #(v^3-10v^2+15v+20)div(v-3)# using synthetic division?
• How do you divide #(r^2+6r+15)div(r+5)# using synthetic division?
• How do you divide #(n^3-5n^2-33n-37)div(n-9)# using synthetic division?
• How do you divide #(x^3+6x^2-30x+102)div(x+10)# using synthetic division?
• How do you divide #(2v^3-20v^2+56v-46)div(v-6)# using synthetic division?
• How do you divide #(m^3-20)div(m-3)# using synthetic division?
• How do you divide #(2k^3-13k^2-77k+60)div(k-10)# using synthetic division?
• How do you divide #(5x^3+11x^2+26x+26)div(5x+6)# using synthetic division?
• How do you divide #(-18a+3a^3+9+6a^2)div(-3+3a)# using synthetic division?
• How do you divide #(3r^3+11r^2-6r-18)div(r+4)# using synthetic division?
• How do you divide #(2n^3+62n-26n^2+4)div(2n-6)# using synthetic division?
• How do you divide #(26-43k-83k^2+9k^3)div(7+9k)# using synthetic division?
• How do you divide #(x^2-2x-15)div(x-5)# using synthetic division?
• How do you divide #(x^3+5x^2+7x+2)div(x+2)# using synthetic division?
• How do you divide #(6x^3+7x^2+12x-5)div(3x-1)# using synthetic division?
• How do you divide #(x^4-81)/(x-3)# using synthetic division?
• How do you divide #(18x^4+9x^3+3x^2)/(3x^2+1)# using synthetic division?
• How do you divide #(5x^3-6x^2+3x+11)div(x-2)# using synthetic division?
• How do you divide #(x^2-5x-5x^3+x^4)div(5+x)# using synthetic division?
• How do you find f(3) given #f(x)=x^3-7x^2+5x-6# using synthetic division?
• How do you divide #(x^2-3x-18)div(x-6)# using synthetic division?
• How do you divide #(2x^4-3x^3+x^2-11)div(x+3)# using synthetic division?
• How do you divide #(x^4+5x^3-2x^2-4x+4)div(x+3)# using synthetic division?
• How do you divide #(4x+2x^3+7x^2-1)div(x+1)# using synthetic division?
• How do you find f(-3) given #f(x)=x^3-2x^2+4x+6# using synthetic division?
• How do you divide #(p^5+5p^3-11p^2-25p+29)div(p+6)# using synthetic division?
• How do you divide #(y^4-8y^3+10y^2+2y+4)div(y-2)# using synthetic division?
• How do you divide #(8v^5+43v^4+5v+20)div(v+4)# using synthetic division?
• How do you divide #(x^3+9x^2+23x+15)div(x+5)# using synthetic division?
• How do you divide #(x^3-x^2-14x+25)div(x-3)# using synthetic division?
• How do you divide #(x^2+5x+1)div(x+3)# using synthetic division?
• How do you divide #(2x^3-11x^2+9x-20)div(x-5)# using synthetic division?
• How do you divide #(2x^3+4x^2-3x-6)div(x+3)# using synthetic division?
• How do you divide #(2x^3-11x^2+13x-44)div(x-5)# using synthetic division?
• How do you divide #(2x^2+4x-4)div(x-2)# using synthetic division?
• How do you divide #(n^4+5n^3-6n+3)div(n+3)# using synthetic division?
• How do you divide #(x^3-125)div(x-5)# using synthetic division?
• How do you divide #(4x^2+3x-1)div(x-3)# using synthetic division?
• How do you divide #(2x^3-x+1)div(x^2+x+1)# using synthetic division?
• How do you divide #(x^3-8x+3)div(x+3)# using synthetic division?
• How do you divide #(x^2+2x+15)div(x-3)# using synthetic division?
• How do you find other zeros given one zero #f(x)=x^3-8x^2+4x+48; 4#?
• How do you divide #(x^3-7x-6)div(x-2)# using synthetic division?
• How do you divide #(3x^2-10x)div(x-6)# using synthetic division?
• How do you divide #(x^2+3)div(x+3)# using synthetic division?
• How do you divide #(10x^4+5x^3+4x^2-9)div(x+1)# using synthetic division?
• How do you divide #(x^4-6x^3-40x+33)div(x-7)# using synthetic division?
• How do you divide #(4x^4+5x^3+2x^2-1)div(x+1)# using synthetic division?
• How do you divide #(x^2+4x+12)div(x-4)#?
• How do you divide #(x^3+6x^2-4x+3)div(x+2)#?
• How do you find the remainder for #(2x^2+x-6)div(x+2)#?
• How do you find the remainder for #(x^3+6x^2-4x+2)div(x+1)#?
• How do you find the remainder for #(x^3+x^2-12x-13)div(x-2)#?
• How do you find the remainder for #(x^4-x^3-3x^2+4x+2)div(x+2)#?
• How do you divide #(x ^ { 2} - 9x + 25) \div ( x - 5)#?
• How do you factor #f(x)=1/4(x^2-2x+15)#?
• How do you divide #(x^3+x^2-17x+15)div(x+5)# using synthetic division?
• How do you divide #(x^3-9x^2+27x-28)div(x-3)# using synthetic division?
• How do you divide #(x^4+x^3-1)div(x-2)# using synthetic division?
• How do you divide #(x^4-8x^2+16)div(x+2)# using synthetic division?
• How do you divide #(3x^4-2x^3+5x^2-4x-2)div(x+1)# using synthetic division?
• How do you divide #(2x^3-2x-3)div(x-1)# using synthetic division?
• How do you find the quotient of #(m^4-2m^3+m^2+12m-6)/(m-2)# using synthetic division?
• How do you find the quotient of #(2-x+x^2-x^3-x^4)div(x+2)# using synthetic division?
• How do you find the quotient of #(2s^3+3s^2-9s-10) div (s-2)# using synthetic division?
• How do you find the quotient of #(h^3+2h^2-3h+9)/(h+3)# using synthetic division?
• How do you find the quotient of #(2x^3+7x^2-x+1)div(x+2)# using synthetic division?
• How do you divide #x^3+7x^2-3x+4) div(x+2)# and identify any restrictions on the variable?
• How do you divide #(x^3+3x^2-2x+5) div(x+1)# and identify any restrictions on the variable?
• How do you divide #(4n^2+7n-5)div(n+3)# and identify any restrictions on the variable?
• Using synthetic division, what is the quotient #(2x^3 + 3x − 22) ÷ (x − 2)#?
• How do you simplify #(5x^4-13x^3+21x^2+x+10)/(5x-3)#?
• How do you use synthetic substitution to find f(3) for #f(x)=x^2 -9x+ 5#?
• How do you use synthetic division to divide #(5x^3+18x^2+7x-6)div(x+3)#?
• How do you use synthetic division to divide #(9x^3-16x-18x^2+32)div(x-2)#?
• How do you use synthetic division to divide #(-x^3+75x-250)div(x+10)#?
• How do you use synthetic division to divide #(5x^3-6x^2+8)div(x-4)#?
• How do you use synthetic division to divide #(5x^3+6x+8)div(x+2)#?
• How do you use synthetic division to divide #(10x^4-50x^3-800)/(x-6)#?
• How do you use synthetic division to divide #(x^5-13x^4-120x+80)/(x+3)#?
• How do you use synthetic division to divide #(x^3+512)/(x+8)#?
• How do you use synthetic division to divide #(x^3-729)/(x-9)#?
• How do you use synthetic division to divide #(-3x^4)/(x-2)#?
• How do you use synthetic division to divide #(-3x^4)/(x+2)#?
• How do you use synthetic division to divide #(180x-x^4)/(x-6)#?
• How do you use synthetic division to divide #(4x^3+16x^2-23x-15)/(x+1/2)#?
• How do you use synthetic division to divide #(3x^3-4x^2+5)/(x-3/2)#?
• How do you use synthetic division to show that x=2 is a zero of #x^3-7x+6=0#?
• How do you use synthetic division to show that x=-4 is a zero of #x^3-28x-48=0#?
• How do you use synthetic division to show that x=1/2 is a zero of #2x^3-15x^2+27x-10=0#?
• How do you use synthetic division to show that #x=sqrt2# is a zero of #x^3+2x^2-2x-4=0#?
• How do you use synthetic division to show that #x=1+sqrt3# is a zero of #x^3-3x^2+2=0#?
• If #(x+2)# is a factor of #x^3-6x^2+kx+10#, what is k?
• How do you use synthetic division #x^4-9x^3+5x^2-7x+10, a=-4#?
• How do you use polynomial synthetic division to divide #(3x^2-2x+1) div(x-1)# and write the polynomial in the form #p(x)=d(x)q(x)+r(x)#?
• How do you use polynomial synthetic division to divide #(x^3+8)div(x+2)# and write the polynomial in the form #p(x)=d(x)q(x)+r(x)#?
• How do you use polynomial synthetic division to divide #(18x^2-15x-25)div(x-5/3)# and write the polynomial in the form #p(x)=d(x)q(x)+r(x)#?
• How do you use polynomial synthetic division to divide #(2x^3+x^2+2x+1)div(x+1/2)# and write the polynomial in the form #p(x)=d(x)q(x)+r(x)#?
• How do you use polynomial synthetic division to divide #(3x^3-x+4)div(x-2/3)# and write the polynomial in the form #p(x)=d(x)q(x)+r(x)#?
• How do you use polynomial synthetic division to divide #(2x^3-3x+1)div(x-1/2)# and write the polynomial in the form #p(x)=d(x)q(x)+r(x)#?
• How do you use polynomial synthetic division to divide #(x^4-6x^2+9)div(x-sqrt3)# and write the polynomial in the form #p(x)=d(x)q(x)+r(x)#?
• How do you use polynomial synthetic division to divide #(x^6-6x^4+12x^2-8)div(x+sqrt2)# and write the polynomial in the form #p(x)=d(x)q(x)+r(x)#?
• How do you divide #(x ^ { 2} - 9x - 10) \div ( x + 1)#?
• How do you divide #\frac { 3x ^ { 4} - 16x ^ { 3} - 4x ^ { 2} + 46x + 7} { x - 5}#?
• Using synthetic division, what is the quotient and the remainder for polynomial #P(x) = x^3 - 2x^2 - 5x +6# divided by #(x-1)#?
• How do you solve #(x^ { 3} - 4x ^ { 2} - 11x + 30 )\div (x - 2)?#