How do you find the quotient of (x^3 + 4x -7) by x-3?

2 Answers
Jim G.
Nov 15, 2017

x^2+3x+13x2+3x+13

Explanation:

"one way is to use the divisor as a factor in the numerator"one way is to use the divisor as a factor in the numerator

"consider the numerator"consider the numerator

color(red)(x^2)(x-3)color(magenta)(+3x^2)+4x-7x2(x−3)+3x2+4x−7

=color(red)(x^2)(x-3)color(red)(+3x)(x-3)color(magenta)(+9x)+4x-7=x2(x−3)+3x(x−3)+9x+4x−7

=color(red)(x^2)(x-3)color(red)(+3x)(x-3)color(red)(+13)(x-3)color(magenta)(+39)-7=x2(x−3)+3x(x−3)+13(x−3)+39−7

=color(red)(x^2)(x-3)color(red)(+3x)(x-3)color(red)(+13)(x-3)+32=x2(x−3)+3x(x−3)+13(x−3)+32

"quotient "=color(red)(x^2+3x+13)," remainder "=32quotient =x2+3x+13, remainder =32

Tony B
Nov 15, 2017

Really this is the same as Jim's solution. It just looks different.

x^2+3x+13+32/(x-3)x2+3x+13+32x−3

Explanation:

Note that I am using a place keepers 0x^20x2. It has no value.

color(white)("dddddddd.ddd.ddd")x^3+0x^2+4x-7dddddddd.ddd.dddx3+0x2+4x−7
color(magenta)(+x^2)color(green)((x-3))->color(white)("ddd") ul(x^3-3x^2 larr" Subtract")
color(white)("ddddddddddddddd")0color(white)("d")+3x^2+4x-7
color(magenta)(+3x)color(green)((x-3))->color(white)("ddddddd") ul(3x^2-9x larr" Subtract")
color(white)("ddddddddddddddddddd") 0color(white)("d")+13x-7
color(magenta)(+13)color(green)((x-3))->color(white)("ddddddddddd")ul(13x-39 larr" Subtract")
color(white)("dddddddddddddddddddddddd")0color(white)("d")color(magenta)(+32 larr" Remainder")

color(magenta)(x^2+3x+13+32/color(green)((x-3))

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