Factor 2x^5+12x^3-54x

$2 x^{5} + 12 x^{3} - 54 x$

Factor $2 x$ out of $2 x^{5} + 12 x^{3} - 54 x$ .

Factor $2 x$ out of $2 x^{5}$ .

$2 x (x^{4}) + 12 x^{3} - 54 x$

Factor $2 x$ out of $12 x^{3}$ .

$2 x (x^{4}) + 2 x (6 x^{2}) - 54 x$

Factor $2 x$ out of $- 54 x$ .

$2 x (x^{4}) + 2 x (6 x^{2}) + 2 x (- 27)$

Factor $2 x$ out of $2 x (x^{4}) + 2 x (6 x^{2})$ .

$2 x (x^{4} + 6 x^{2}) + 2 x (- 27)$

Factor $2 x$ out of $2 x (x^{4} + 6 x^{2}) + 2 x (- 27)$ .

$2 x (x^{4} + 6 x^{2} - 27)$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$2 x ({(x^{2})}^{2} + 6 x^{2} - 27)$

Let $u = x^{2}$ . Substitute $u$ for all occurrences of $x^{2}$ .

$2 x (u^{2} + 6 u - 27)$

Factor $u^{2} + 6 u - 27$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 27$ and whose sum is $6$ .

$- 3, 9$

Write the factored form using these integers.

$2 x ((u - 3) (u + 9))$

Factor.

Replace all occurrences of $u$ with $x^{2}$ .

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

Remove unnecessary parentheses.

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

Factor 2x^5+12x^3-54x

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