Algebra Examples

$2 x^{2} + 10 x + 12$

Step 1

Factor $2$ out of $2 x^{2} + 10 x + 12$ .

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Step 1.1

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

$2 (x^{2}) + 10 x + 12$

Step 1.2

Factor $2$ out of $10 x$ .

$2 (x^{2}) + 2 (5 x) + 12$

Step 1.3

Factor $2$ out of $12$ .

$2 x^{2} + 2 (5 x) + 2 \cdot 6$

Step 1.4

Factor $2$ out of $2 x^{2} + 2 (5 x)$ .

$2 (x^{2} + 5 x) + 2 \cdot 6$

Step 1.5

Factor $2$ out of $2 (x^{2} + 5 x) + 2 \cdot 6$ .

$2 (x^{2} + 5 x + 6)$

Step 2

Factor.

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Step 2.1

Factor $x^{2} + 5 x + 6$ 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 $6$ and whose sum is $5$ .

$2, 3$

Step 2.1.2

Write the factored form using these integers.

$2 ((x + 2) (x + 3))$

Step 2.2

Remove unnecessary parentheses.

$2 (x + 2) (x + 3)$