I'm reviewing my algebra in prep for Linear Algebra, using the review of Algebra in Stewart's Single Variable Calculus, here: http://stewartcalculus.com/data/CALCULUS_8E_ET/upfiles/6et_reviewofalgebra.pdf
On p.4, they use the Factor Theorem to factor $$x^3 - 3x^2 -10x + 24$$
They state the following:
If P(b) = 0, where b is an integer, then b is a factor of 24.
They then use this fact to test possible integer values of b as a factor of 24 (+1, -1, +2, -2, etc.). What I'm not understanding is how they arrive at the fact that b must be a factor of 24 based on the the Factor Theorem. I understand from the Factor Theorem that if P(b) = 0, then x - b will be a factor of P(x), but how did they discern that b would be a factor of 24? Thanks in advance.