Factor 14x^2+30x+4

$14 x^{2} + 30 x + 4$

Step 1

Factor $2$ out of $14 x^{2} + 30 x + 4$ .

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

$2 (7 x^{2}) + 30 x + 4$

Factor $2$ out of $30 x$ .

$2 (7 x^{2}) + 2 (15 x) + 4$

Factor $2$ out of $4$ .

$2 (7 x^{2}) + 2 (15 x) + 2 (2)$

Factor $2$ out of $2 (7 x^{2}) + 2 (15 x)$ .

$2 (7 x^{2} + 15 x) + 2 (2)$

Factor $2$ out of $2 (7 x^{2} + 15 x) + 2 (2)$ .

$2 (7 x^{2} + 15 x + 2)$

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 $a \cdot c = 7 \cdot 2 = 14$ and whose sum is $b = 15$ .

Factor $15$ out of $15 x$ .

$2 (7 x^{2} + 15 (x) + 2)$

Rewrite $15$ as $1$ plus $14$

$2 (7 x^{2} + (1 + 14) x + 2)$

Apply the distributive property.

$2 (7 x^{2} + 1 x + 14 x + 2)$

Multiply $x$ by $1$ .

$2 (7 x^{2} + x + 14 x + 2)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((7 x^{2} + x) + 14 x + 2)$

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

$2 (x (7 x + 1) + 2 (7 x + 1))$

Factor the polynomial by factoring out the greatest common factor, $7 x + 1$ .

$2 ((7 x + 1) (x + 2))$

Remove unnecessary parentheses.

$2 (7 x + 1) (x + 2)$

Factor 14x^2+30x+4

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