# How do you factor x^3+2x^2-8x-16?

May 9, 2015

Try x = -2.
$f \left(- 2\right) = - 8 + 8 + 16 - 16 = 0.$Then f(x) can be divided by (x + 2)

$f \left(x\right) = \left(x + 2\right) \left({x}^{2} - 8\right) .$

May 9, 2015

The answer is $\left({x}^{2} - 8\right) \left(x + 4\right)$ .

Factor ${x}^{3} + 2 {x}^{2} - 8 x - 16$ .

Since there is no common factor for the polynomial, factor by grouping.

color(red)(x^3+2x^2)color(blue)(-(8x-16)

Factor ${\textcolor{red}{x}}^{2}$ out of the first term.

color(red)(x^2(x+2)

Factor color(blue)(-8 out of the second term.

color(blue)(-8(x+2)

Put the two sets of terms back together.

color(red)(x^2(x+2)color(blue)(-8(x+2)

color(purple)((x+2) is now the common factor.

Factor out color(purple)((x+2) .

Final answer = color(purple)((x^2-8)(x+2)#