Factor 2x^2-28x+98

$2 x^{2} - 28 x + 98$

Step 1

Factor $2$ out of $2 x^{2} - 28 x + 98$ .

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

$2 (x^{2}) - 28 x + 98$

Factor $2$ out of $- 28 x$ .

$2 (x^{2}) + 2 (- 14 x) + 98$

Factor $2$ out of $98$ .

$2 x^{2} + 2 (- 14 x) + 2 \cdot 49$

Factor $2$ out of $2 x^{2} + 2 (- 14 x)$ .

$2 (x^{2} - 14 x) + 2 \cdot 49$

Factor $2$ out of $2 (x^{2} - 14 x) + 2 \cdot 49$ .

$2 (x^{2} - 14 x + 49)$

Step 2

Factor using the perfect square rule.

Rewrite $49$ as $7^{2}$ .

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

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

$14 x = 2 \cdot x \cdot 7$

Rewrite the polynomial.

$2 (x^{2} - 2 \cdot x \cdot 7 + 7^{2})$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 7$ .

$2 {(x - 7)}^{2}$