Long Division

Question

Divide by using long division: (6x^3 + 5x -8) / (x-2)

Answer 1

 (6x^3 + 5x -8) / (x-2)

 

Set up like a regular division problem.  In each case you will multiply the x term of (x-2)

by whatever value will make it equal to the first term in the appropriate line then subtract from

the previous line.

 

             6x²  + 12x  + 29

          __________________________

(x-2)  /  6x³             + 5x             -8

          -(6x³ -12x²)                             Note (6x²)(x-2) = 6x³-12x²

          ----------------------------------

                   12x²   + 5x         -8 

                 -(12x²    -24x)                    Note (12x)(x-2) = 12x²-24x

                 -------------------------

                              29x  -   8

                            -(29x  - 58)            Note (29)(x-2) = 29x - 58

                            --------------

                                         50

 

Stop at the point where the difference has a lower exponent than the divisor and write

the remainder as R/(x-2)

 

(6x^3 + 5x -8) / (x-2) =   6x²  + 12x  + 29 + 50/(x-2)