How do you divide #(3x^3+4x^2+x+1)÷(x-1)#?

1 Answer

#3x^2+7x+8+(9)/(x-1)#

Explanation:

You can use Remainder Theorem or Synthetic Division to do so. I will use the Synthetic Division since it is quicker and easier (but it only works for a polynomial divided by a binomial).

The first step in using theSynthetic Division is to find out what makes the binomial #0#. In this case, it is #1#. Now, you put that number in a sort of secluded area like so:

#1" "|#

Then, you determine the co-efficients for every term in your polynomial (you MUST also include co-efficients of #0#. However, there are none in this problem). Then, you make a list like this:

#1" "|color(white)(xx)3" " "4" " "1color(white)(xx)1#

Then, you do this little trick where you bring down the first number (#3#), multiply by the secluded number (#1#), put the answer down under the next number (#4#), and then add. After its all done, it'll look like this:

#1" "|color(white)(xx)3" " "4" " "1color(white)(xx)1#
#color(white)(xxxxxx)darrcolor(white)(x)3" " "7color(white)(xx)8#
#color(white)(xxxxx)stackrel("---------------------------------")#
#color(white)(xxxxxx)3" " "7" " "8|color(white)(x)9#

Now, the remainder has the co-efficients on the third line (#3#, #7#, and #8#), making the polynomial #3x^2+7x+8#. The #9# is the remainder (divided by the binomial).

All-in-all, the answer is:

#3x^2+7x+8+(9)/(x-1)#.

I know the description was confusing, which is why I have attached a link to a video that will do a better job explaining it to you!