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

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Answer 1 · 2017-01-08T16:35:49

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

We use

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

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

Therefore, we start factorising

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

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

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

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

How do you factor 9x^3+36x^2-4x-169x3+36x2−4x−169x^3+36x^2-4x-16?