Question

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

Answer 1

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 `(x+a)^2`.

Since we want `a^2=36` and `2a=12`, we want to use `a=6` so the factorization is `x^2+12x+36=(x+6)^2`.