(12x3 + 3x2 - 108) (3x - 6)

Question

Use long division to find the quotient below. Enter your answer as a polynomial in descending order, using the caret ( ^ ) for exponents; for example, enter x² as x^2.

Answer 1

To simplify the problem, divide dividend and divisor by their common factor 3:

(4x³+x²-36)/(x-2) can be solved by synthetic division:

2 | 4 1   0  -36

     4 8 18 | 36

     4 9 18 |   0 = 4x²+9x+18.

Using algebraic division:

         4x²+9x+18

x-2 ) 4x³ +x²       -36

        4x³-8x²

              9x²

              9x²-18x

                     18x-36 

                     18x-36

                           0