Question

If $(x + 4)$ is a factor of $x^3 + 2x^2 + bx + 68$, what is the value of b?

Accepted Answer

B. By the Factor Theorem, if $(x + 4)$ is a factor, then $f(-4) = 0$. $f(-4) = (-4)^3 + 2(-4)^2 + b(-4) + 68 = 0$ $-64 + 32 - 4b + 68 = 0 \implies 36 - 4b = 0 \implies b = 9$.

Factor theorem polynomial coefficient

Explanation

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