Algebra Examples

Factor $2 x^{2} + 4 x - 30$

Step 1

Factor $2$ out of $2 x^{2} + 4 x - 30$ .

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Step 1.1

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

$2 (x^{2}) + 4 x - 30$

Step 1.2

Factor $2$ out of $4 x$ .

$2 (x^{2}) + 2 (2 x) - 30$

Step 1.3

Factor $2$ out of $- 30$ .

$2 x^{2} + 2 (2 x) + 2 \cdot - 15$

Step 1.4

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

$2 (x^{2} + 2 x) + 2 \cdot - 15$

Step 1.5

Factor $2$ out of $2 (x^{2} + 2 x) + 2 \cdot - 15$ .

$2 (x^{2} + 2 x - 15)$

Step 2

Factor.

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Step 2.1

Factor $x^{2} + 2 x - 15$ using the AC method.

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Step 2.1.1

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 $- 15$ and whose sum is $2$ .

$- 3, 5$

Step 2.1.2

Write the factored form using these integers.

$2 ((x - 3) (x + 5))$

Step 2.2

Remove unnecessary parentheses.

$2 (x - 3) (x + 5)$