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

To determine if $x + 9$ is a factor of $f(x) = x^3 + 7x^2 - 16x + 18$, we use the Factor Theorem by evaluating $f(-9)$. If $f(-9) = 0$, then $x + 9$ is a factor. Substituting $-9$ into $f(x)$ gives $f(-9) = (-9)^3 + 7(-9)^2 - 16(-9) + 18 = -729 + 567 + 144 + 18 = 0$. Since $f(-9) = 0$, $x + 9$ is indeed 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 $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 16 x + 18 ; x + 9$