Factor 4x^2+6x+2

$4 x^{2} + 6 x + 2$

Step 1

Factor $2$ out of $4 x^{2} + 6 x + 2$ .

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

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

Factor $2$ out of $6 x$ .

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

Factor $2$ out of $2$ .

$2 (2 x^{2}) + 2 (3 x) + 2 (1)$

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

$2 (2 x^{2} + 3 x) + 2 (1)$

Factor $2$ out of $2 (2 x^{2} + 3 x) + 2 (1)$ .

$2 (2 x^{2} + 3 x + 1)$

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 $a \cdot c = 2 \cdot 1 = 2$ and whose sum is $b = 3$ .

Factor $3$ out of $3 x$ .

$2 (2 x^{2} + 3 (x) + 1)$

Rewrite $3$ as $1$ plus $2$

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

Apply the distributive property.

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

Multiply $x$ by $1$ .

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Remove unnecessary parentheses.

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

Factor 4x^2+6x+2

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