Factor 2x^3+2x^2-24x

$2 x^{3} + 2 x^{2} - 24 x$

Step 1

Factor $2 x$ out of $2 x^{3} + 2 x^{2} - 24 x$ .

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

$2 x (x^{2}) + 2 x^{2} - 24 x$

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

$2 x (x^{2}) + 2 x (x) - 24 x$

Factor $2 x$ out of $- 24 x$ .

$2 x (x^{2}) + 2 x (x) + 2 x (- 12)$

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

$2 x (x^{2} + x) + 2 x (- 12)$

Factor $2 x$ out of $2 x (x^{2} + x) + 2 x (- 12)$ .

$2 x (x^{2} + x - 12)$

Step 2

Factor.

Factor $x^{2} + x - 12$ 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 $- 12$ and whose sum is $1$ .

$- 3, 4$

Write the factored form using these integers.

$2 x ((x - 3) (x + 4))$

Remove unnecessary parentheses.

$2 x (x - 3) (x + 4)$

Factor 2x^3+2x^2-24x

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