Use the remainder theorem to find which of the following is not a factor of x3 + 12x2 + 47x + 60

Question

the answer is x-5 but idk why

Answer 1

The remainder theorem states that

f(x) = (x-p)*q(x) + f(p)

So, if f(p)=0, (x-p) divides f(x) evenly; it is a factor.

f(5) = 5^3 + 12*5^2 + 47*5 + 60 = 720

so, f(x) = (x-5)*q(x) + 720

for some q(x)