Factor the polynomial completely given that p(k)=0. p(x)= x^3+2x^2-5x-6 ; k=-1

The three factors of the given polynomial are (x + 3), (x - 2) and (x + 1).

Step-by-step explanation:

Use synthetic division here.  If synthetic division results in a zero remainder, then the synthetic division divisor is a root of the polynomial and the corresponding factor is easily found from it.

Using k = -1 as divisor:

-1    /    1    2    -5    -6

               -1      -1      6

           1      1      -6     0

Here the remainder is 0, so we know that the corresponding factor of this polynomial is (x + 1).  The remaining factors can be found by factoring x^2 + x - 6:  x^2 + x - 6 =  (x + 3)(x - 2)

The three factors of the given polynomial are (x + 3), (x - 2) and (x + 1).