How do you divide #(x^3+2x^2-11x-12)/(x^2-3x+2)#?

Question

Sadie Alexander · Accepted Answer

Long divide coefficients to find:

#(x^3+2x^2-11x-12)/(x^2-3x+2) = x+5+(2x-22)/(x^2-3x+2)#

You can just divide the coefficients like this:

The process is similar to long division of numbers.

Note that if there were any 'missing' powers of #x# in the dividend or divisor then we would have to include #0#'s for them.

Write the dividend #1,2,-11,-12# under the bar and the divisor #1,-3,2# to the left.

Choose the first term #color(blue)(1)# of the quotient so that when multiplied by the divisor, the resulting leading term (#1#) matches the leading term (#1#) of the dividend.

Write the product #1,-3,2# of this first term of the quotient and the divisor under the dividend and subtract to give a remainder #5,-13#.

Bring down the next term #-12# from the dividend alongside it to give your running remainder #5,-13,-12#.

Choose the next term #color(blue)(5)# of the quotient so that when multiplied by the divisor, the resulting leading term (#5#) matches the leading term (#5#) of the remainder.

Write the product #5,-15,10# of this second term of the quotient and the divisor under the running remainder and subtract to give a remainder #2,-22#.

There are no more terms to bring down from the dividend, so this is our final remainder.

We find:

#(x^3+2x^2-11x-12)/(x^2-3x+2) = x+5+(2x-22)/(x^2-3x+2)#

Christian Antunez · Answer

undefined To divide $ \frac{x^3 + 2x^2 - 11x - 12}{x^2 - 3x + 2} $, perform polynomial long division or synthetic division. Set up the division, divide each term of the dividend by the divisor, and then subtract to find the remainder. Keep dividing until you have a remainder with a degree less than that of the divisor, or until you have a constant remainder. The result of the division will be the quotient plus any remainder, if present.