How can I solve this?

Question

(4x^3+6x^2-2x+3)/(x+2)

Answer 1

IF YOU HAVE LEARNED SYNTHETIC DIVISION*, this problem can be done that way; put -1 in the dividing notch.

Otherwise, use method that Andrew specified.

 

 

*  Synthetic division is usually introduced in an Algebra II course.

 

Answer 2

You can do this as a long division problem

 

         4x² -2x + 2

        ---------------------

x+2 /   4x³+6x²-2x+3    multiply by 4x²

        -(4x³+8x²)          subtract the product

       -----------------   

              -2x²-2x+3   multiply by -2x

            -(-2x²-4x)      subtract the product

         -----------------

                    2x + 3   multiply by 2

                  -(2x + 4) subtract the product

                -------------

                           -1   remainder

 

Once the highest exponent on the difference is lower

than that on the expression you are dividing by you

are done

 

your answer is: 4x²-2x+2 - 1/(x+2)