Factor 2a^2+14a+12

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

Step 1

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

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

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

Factor $2$ out of $14 a$ .

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

Factor $2$ out of $12$ .

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

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

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

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

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

Step 2

Factor.

Factor $a^{2} + 7 a + 6$ 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 $6$ and whose sum is $7$ .

$1, 6$

Write the factored form using these integers.

$2 ((a + 1) (a + 6))$

Remove unnecessary parentheses.

$2 (a + 1) (a + 6)$

Factor 2a^2+14a+12

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