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

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Answer 1 · 2016-08-28T15:35:04

$x^3+2x^2-8x-16=(x-2sqrt(2))(x+2sqrt(2))(x+2)$

Given:

$x^3+2x^2-8x-16$

Notice that the ratio between the first and second terms is the same as that between the third and fourth terms.

So this cubic will factor by grouping:

$x^3+2x^2-8x-16$

$=(x^3+2x^2)-(8x+16)$

$=x^2(x+2)-8(x+2)$

$=(x^2-8)(x+2)$

$=(x^2-(2sqrt(2))^2)(x+2)$

$=(x-2sqrt(2))(x+2sqrt(2))(x+2)$

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