synthetic Division?

Question

Is (x - 2) a factor of x3 + 2x2 - 5x - 6?

 

I have to show my work using Synthetic Division 

Answer 1

              1   4    3

1 -2 ) 1   2  -5  -6

         1  -2

              4  -5

              4  -8

                   3  -6

                   3  -6

                        0

 

The remainder is 0 so x - 2 is a factor.

 

Fact:

The quotient x² + 4x + 3 also factors so x³ + 2x² - 5x - 6 = (x - 2)(x + 1)(x + 3).