# What Factor Theorem Do You Know?

Algebra Level 3

$\large P(x) =x^3+2x^2 + 2x + c \qquad\qquad Q(x) = x^2 + bx + b$

Consider the polynomials $$P(x)$$ and $$Q(x)$$ above, where $$b$$ and $$c$$ are constant real numbers and $$c\ne0$$.

It is known that $$Q(x)$$ is a factor of $$P(x)$$. Find the value of $$b+c$$.

×