What Factor Theorem Do You Know?

Algebra Level 3

P(x)=x3+2x2+2x+cQ(x)=x2+bx+b \large P(x) =x^3+2x^2 + 2x + c \qquad\qquad Q(x) = x^2 + bx + b

Consider the polynomials P(x)P(x) and Q(x)Q(x) above, where bb and cc are constant real numbers and c0c\ne0 .

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

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