Factor x^2-26x+169

$x^{2} - 26 x + 169$

Step 1

Rewrite $169$ as $13^{2}$ .

$x^{2} - 26 x + 13^{2}$

Step 2

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

$26 x = 2 \cdot x \cdot 13$

Step 3

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 13 + 13^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 13$ .

${(x - 13)}^{2}$