Factor 8x^2+16x+6

$8 x^{2} + 16 x + 6$

Step 1

Factor $2$ out of $8 x^{2} + 16 x + 6$ .

Factor $2$ out of $8 x^{2}$ .

$2 (4 x^{2}) + 16 x + 6$

Factor $2$ out of $16 x$ .

$2 (4 x^{2}) + 2 (8 x) + 6$

Factor $2$ out of $6$ .

$2 (4 x^{2}) + 2 (8 x) + 2 (3)$

Factor $2$ out of $2 (4 x^{2}) + 2 (8 x)$ .

$2 (4 x^{2} + 8 x) + 2 (3)$

Factor $2$ out of $2 (4 x^{2} + 8 x) + 2 (3)$ .

$2 (4 x^{2} + 8 x + 3)$

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 $a \cdot c = 4 \cdot 3 = 12$ and whose sum is $b = 8$ .

Factor $8$ out of $8 x$ .

$2 (4 x^{2} + 8 (x) + 3)$

Rewrite $8$ as $2$ plus $6$

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$2 (2 x (2 x + 1) + 3 (2 x + 1))$

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$2 ((2 x + 1) (2 x + 3))$

Remove unnecessary parentheses.

$2 (2 x + 1) (2 x + 3)$

Factor 8x^2+16x+6

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