Answer
$r^2-11r+24=(r-8)(r-3)$
Work Step by Step
$r^2-11r+24$
Factors of 24 | Sum of Factors
$\ \ \ \ \ \ 1,24\ \ \ \ \ \ \ |\ \ \ \ \ \ \ \ \ \ 25$
$\ \ \ \ \ \ 2,12\ \ \ \ \ \ \ |\ \ \ \ \ \ \ \ \ \ 14$
$\ \ \ \ \ \ 4,6\ \ \ \ \ \ \ \ \ |\ \ \ \ \ \ \ \ \ \ 10$
$\ \ \ \ \ \ 8,3\ \ \ \ \ \ \ \ \ |\ \ \ \ \ \ \ \ \ \ 11\checkmark$
Since the second term in the binomial is subtracted (or negative) and the third term is positive, the factors will both include subtraction.
$r^2-11r+24=(r-8)(r-3)$
Use the FOIL method to check the answer.
$(r-8)(r-3)=r^2-3r-8r+24=r^2-11r+24\checkmark$
