Answer
$(x-4)(x-8)$
Work Step by Step
In order to factor $x^{2}-12x+32$, we must find a pair of negative numbers whose product is equal to 32 (or the constant term) and whose sum is equal to -12 (or the coefficient on the middle term).
We know that the pairs of negative numbers whose product is 32 are -1,-32, -2,-16, and -4,-8.
Out of these pairs, the sum of -4 and -8 is equal to -12.
Therefore, $x^{2}-12x+32=(x-4)(x-8)$.
