Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18 ; x + 9$
A) Yes
B) No

Question

Quizplus · Accepted Answer

The Factor Theorem states that $x - c$ is a factor of $f(x)$ if and only if $f(c) = 0$. Given $x + 9$, we have $c = -9$. Substituting $x = -9$ into $f(x)$, we get $f(-9) = (-9)^3 + 7(-9)^2 - 16(-9) + 18 = -729 + 567 + 144 + 18 = 0$. Since $f(-9) = 0$, $x + 9$ is a factor of $f(x)$.

Use the Factor Theorem to Determine Whether X - C f(x)=x3+7x2−16x+18;x+9f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18 ; x + 9f(x)=x3+7x2−16x+18;x+9

Use the Factor Theorem to Determine Whether X - C $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18 ; x + 9$