Answer
$q^2-8q+12=(q-2)(q-6)$
Work Step by Step
$q^2-8q+12$
Factors of 12 | Sum of Factors
$\ \ \ \ \ \ 1,12\ \ \ \ \ \ \ |\ \ \ \ \ \ \ \ \ \ 13$
$\ \ \ \ \ \ 2,6\ \ \ \ \ \ \ \ \ |\ \ \ \ \ \ \ \ \ \ \ \ 8\checkmark$
$\ \ \ \ \ \ 4,3\ \ \ \ \ \ \ \ \ |\ \ \ \ \ \ \ \ \ \ \ \ 7$
Since the second term in the binomial is subtracted (or negative) and the third term is positive, the factors will both include subtraction.
$q^2-8q+12=(q-2)(q-6)$
Use the FOIL method to check the answer.
$(q-2)(q-6)=q^2-6q-2q+12=q^2-8q+12\checkmark$
