3x3 - 3x2 - 4x + 3 divided by x + 3

Question

We're doing division of polynomials, and I'm really confused on how to do it

Answer 1

 

                   3x²- 12x+32

       -------------------------

x+3 | 3x³ - 3x² - 4x + 3           Compare the x in the divisor to the first term of the dividend, x and 3x³.  x(3x²) = 3x³     

         3x³+ 9x²                             Multiply each term in the divisor by 3x²

        ---------------------

                -12x² - 4x                  Subtract each term.  Now x(-12x) = -12x²

                -12x²- 36x                  Multiply each term in the divisor by -12x

        ----------------------

                        32x + 3           Subtract each term. Now x(32) = 32x

                        32x +96         Multiply each term in the divisor by 32

         ----------------------

                               -93           Subtract each term

 

The quotient is

3x² - 12x + 32  remainder -93 or

3x² - 12x + 32 - 93/(x+3)