## Intermediate Algebra (6th Edition)

$(x-6)^2$
The two numbers whose product is $36$ and whose sum is $-12$ are $\{ -6,-6\}$. Using these numbers to decompose the middle term of the trinomial, then, \begin{array}{l} x^2-12x+36 \\= x^2-6x-6x+36 \\= (x^2-6x)-(6x-36) \\= x(x-6)-6(x-6) \\= (x-6)(x-6) \\= (x-6)^2 .\end{array}