x^3+x^2-16x-16 factor:x+2

Question

 determine it is factor or not

Answer 1

Divide the polynomial by (x + 2).  If we divide by long division, the remainder must be zero in order for (x + 2) to be a factor.

 

 

We can also divide by factoring the polynomial and then cancelling out terms until we can not longer factor.  Lets try this method first before using long division.

 

 

(x³ + x² - 16x - 16) / (x + 2) =

 

[x²(x + 1) - 16(x + 1)] / (x + 2) =

 

[(x² - 16)(x + 1)] / (x + 2) =

 

[(x + 4)(x - 4)(x + 1)] / (x + 2)

 

 

We cannot cancel out any terms.  Therefore, we need to use long division as an alternative method.

 

 

                      x²  -  x  -  14

            ___________________

(x + 2) | x³ +  x² - 16x - 16

             x³ + 2x²

            _____________

                  - x² - 16x

                  - x² -  2x

                 ____________

                        - 14x - 16

                        - 14x - 28

                       __________

                                   12

 

 

The remainder is 12.  Therefore, (x + 2) is not a factor.