Factor 4x^2+14x+12

$4 x^{2} + 14 x + 12$

Step 1

Factor $2$ out of $4 x^{2} + 14 x + 12$ .

Factor $2$ out of $4 x^{2}$ .

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

Factor $2$ out of $14 x$ .

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

Factor $2$ out of $12$ .

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

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

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

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

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

Step 2

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 2 \cdot 6 = 12$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

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

Rewrite $7$ as $3$ plus $4$

$2 (2 x^{2} + (3 + 4) x + 6)$

Apply the distributive property.

$2 (2 x^{2} + 3 x + 4 x + 6)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((2 x^{2} + 3 x) + 4 x + 6)$

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $2 x + 3$ .

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

Remove unnecessary parentheses.

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

Factor 4x^2+14x+12

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