Factor 2x^2+4x+2

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

Step 1

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

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

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

Factor $2$ out of $4 x$ .

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

Factor $2$ out of $2$ .

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

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

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

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

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

Step 2

Factor using the perfect square rule.

Rewrite $1$ as $1^{2}$ .

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

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 x = 2 \cdot x \cdot 1$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 1$ .

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