Question

Factor x^3 +2x^2 -9x -18, given that -2 is a zero

Answer 1

(x-2)(x-3)(x+3)are the factors of the given expression.

Explanation:

We have given the expression:

x³ +2x² -9x -18

And we have given that -2 is the zero of the given expression.

We have to find the other factors of this expression.

Taking common from the given expression we get,

x³ +2x² -9x -18 = x²(x-2)-9(x-2)

Taking (x-2) common from x²(x-2)-9(x-2) we get,

x²(x-2)-9(x-2) = (x-2)(x²-9)

As we know that,

(x²-9) = (x-3)(x+3)

(x-2)(x²-9) = (x-2)(x-3)(x+3)

(x-2)(x-3)(x+3)are the factors of the given expression.

Answer 2

Explanation:

Take out the common factor from the first and second terms and again from the 3rd and fourth terms.

x^2(x + 2) - 9(x + 2)

Take out x + 2 from around the minus sign.

(x + 2)(x^2 - 9)

Factor x^2 - 9 which will come out to the difference of squares.

(x + 2)(x + 3)(x - 3)

This is how it factors.

You could also use synthetic division if you know how it works.

-2 || 1 2 -9 -18

-2 0 18

====================

1 0 -9 0

This gives you (x + 2)(x^3 - 9) just as before.