# How do you factor a perfect square trinomial X ²+12 X +36?

Since (we're implicitly assuming) it's a perfect square and the coefficient of the highest power is 1, it's just a matter of guessing factorizations of the form ${\left(x + a\right)}^{2}$.
Since we want ${a}^{2} = 36$ and $2 a = 12$, we want to use $a = 6$ so the factorization is ${x}^{2} + 12 x + 36 = {\left(x + 6\right)}^{2}$.