Factor x^2+24x+144

$x^{2} + 24 x + 144$

Step 1

Rewrite $144$ as $12^{2}$ .

$x^{2} + 24 x + 12^{2}$

Step 2

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

$24 x = 2 \cdot x \cdot 12$

Step 3

Rewrite the polynomial.

$x^{2} + 2 \cdot x \cdot 12 + 12^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 12$ .

${(x + 12)}^{2}$