Pre-Algebra Examples

$2 x^{2} + 14 x + 12$

Step 1

Factor $2$ out of $2 x^{2} + 14 x + 12$ .

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Step 1.1

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

$2 (x^{2}) + 14 x + 12$

Step 1.2

Factor $2$ out of $14 x$ .

$2 (x^{2}) + 2 (7 x) + 12$

Step 1.3

Factor $2$ out of $12$ .

$2 x^{2} + 2 (7 x) + 2 \cdot 6$

Step 1.4

Factor $2$ out of $2 x^{2} + 2 (7 x)$ .

$2 (x^{2} + 7 x) + 2 \cdot 6$

Step 1.5

Factor $2$ out of $2 (x^{2} + 7 x) + 2 \cdot 6$ .

$2 (x^{2} + 7 x + 6)$

Step 2

Factor.

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Step 2.1

Factor $x^{2} + 7 x + 6$ 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 $7$ .

$1, 6$

Step 2.1.2

Write the factored form using these integers.

$2 ((x + 1) (x + 6))$

Step 2.2

Remove unnecessary parentheses.

$2 (x + 1) (x + 6)$