Question

X^3 + 2x^2 - 9x - 18

Answer 1

The expression is given to be:

`x^3\: +\: 2x^2\: -\: 9x\: -\: 18`

Divide the expression:

`(x^3\: +\: 2x^2\: )+(-\: 9x\: -\: 18)`

Collect like terms in each parenthesis:

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

Factorize (x + 2) from the expression:

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

Recall the difference of two squares given to be:

`x^2-a^2=(x-a)(x+a)`

Therefore, we have:

`x^2-9=x^2-3^2=(x-3)(x+3)_{}`

Hence, the completely factorized expression is:

`\Rightarrow(x+2)(x-3)(x+3)`