Factor $36 x^{3} + 12 x^{2} - 72 x - 24$ $36x^3+12x^2-72x-24$ ?

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Factor $36 x^{3} + 12 x^{2} - 72 x - 24$ $36x^3+12x^2-72x-24$ ?

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Answer 1 · 2016-12-21T00:07:39

$36 x^{3} + 12 x^{2} - 72 x - 24 = 12 (x - \sqrt{2}) (x + \sqrt{2}) (3 x + 1)$ $36x^3+12x^2-72x-24 = 12(x-sqrt(2))(x+sqrt(2))(3x+1)$

Explanation:

Note that the ratio of the $1$ $1$ st and $2$ $2$ nd terms is the same as that between the $3$ $3$ rd and $4$ $4$ th terms. So this cubic will factor by grouping. Also note that all of the coefficients are divisible by $12$ $12$ , so we can separate that out as a factor first:

$36 x^{3} + 12 x^{2} - 72 x - 24 = 12 (3 x^{3} + x^{2} - 6 x - 2)$ $36x^3+12x^2-72x-24 = 12(3x^3+x^2-6x-2)$

$36 x^{3} + 12 x^{2} - 72 x - 24 = 12 ((3 x^{3} + x^{2}) - (6 x + 2))$ $color(white)(36x^3+12x^2-72x-24) = 12((3x^3+x^2)-(6x+2))$

$36 x^{3} + 12 x^{2} - 72 x - 24 = 12 (x^{2} (3 x + 1) - 2 (3 x + 1))$ $color(white)(36x^3+12x^2-72x-24) = 12(x^2(3x+1)-2(3x+1))$

$36 x^{3} + 12 x^{2} - 72 x - 24 = 12 (x^{2} - 2) (3 x + 1)$ $color(white)(36x^3+12x^2-72x-24) = 12(x^2-2)(3x+1)$

$36 x^{3} + 12 x^{2} - 72 x - 24 = 12 (x^{2} - {(\sqrt{2})}^{2}) (3 x + 1)$ $color(white)(36x^3+12x^2-72x-24) = 12(x^2-(sqrt(2))^2)(3x+1)$

$36 x^{3} + 12 x^{2} - 72 x - 24 = 12 (x - \sqrt{2}) (x + \sqrt{2}) (3 x + 1)$ $color(white)(36x^3+12x^2-72x-24) = 12(x-sqrt(2))(x+sqrt(2))(3x+1)$

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Factor $36 x^{3} + 12 x^{2} - 72 x - 24$ $36x^3+12x^2-72x-24$ ?

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Explanation:

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Factor 36x^3+12x^2-72x-2436x3+12x2−72x−2436x^3+12x^2-72x-24 ?

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Factor $36 x^{3} + 12 x^{2} - 72 x - 24$ $36x^3+12x^2-72x-24$ ?