#### Answer

$(x-3)(x-9)$

#### Work Step by Step

In order to factor $x^{2}-12x+27$, we must find a pair of negative numbers whose product is equal to 27 (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 27 are -1,-27 and -3,-9.
Out of these pairs, the sum of -3 and -9 is equal to -12.
Therefore, $x^{2}-12x+27=(x-3)(x-9)$.