Question

One factor of x3 + 2x2 -x -2 is x+2 . Find two other factors of this polynomial.

Answer 1

x^3+2x^2-x-2=(x+2)(x-1)(x+1)

The other two factors are x-1 and x+1

Explanation:

Use synthetic division:

x^3+2x^2-x-2 / x+2

-2 | 1 2 -1 -2

-2 0 2

_________

1 0 -1 0

This means x^2-1 with no remainder, but we can still break it down. The factors of -1 are 1 and -1, so we must find the factors:

1 | 1 0 -1

1 1

______

1 1 0

This means x+1 so that's one factor

-1 | 1 0 -1

-1 1

_______

1 -1 0

This means x-1 so that's the other factor

Thus, the factors of x^3+2x^2-x-2 are (x+2)(x+1)(x-1)