Factor y=x^3+x^2-12x

$y = x^{3} + x^{2} - 12 x$

Step 1

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

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

$y = x \cdot x^{2} + x^{2} - 12 x$

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

$y = x \cdot x^{2} + x \cdot x - 12 x$

Factor $x$ out of $- 12 x$ .

$y = x \cdot x^{2} + x \cdot x + x \cdot - 12$

Factor $x$ out of $x \cdot x^{2} + x \cdot x$ .

$y = x (x^{2} + x) + x \cdot - 12$

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

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

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.

$y = x ((x - 3) (x + 4))$

Remove unnecessary parentheses.

$y = x (x - 3) (x + 4)$

Factor y=x^3+x^2-12x

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