How do you factor $9x^3+36x^2-4x-16$ ?

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Answer 1 · 2017-01-08T16:35:49

The answer is $=color(red)((x+4))color(blue)((3x+2)(3x-2))$

We use

$a^2-b^2=(a+b)(a-b)$

$9x^2-4=(3x+2)(3x-2)$

Therefore, we start factorising

$9x^3+36x^2-4x-16$

$=9x^2color(red)((x+4))-4color(red)((x+4))$

$=color(red)((x+4))color(blue)((9x^2-4))$

$=color(red)((x+4))color(blue)((3x+2)(3x-2))$

How do you factor 9x^3+36x^2-4x-169x^3+36x^2-4x-16?