Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$f ( x ) = 56 x ^ { 3 } + 61 x ^ { 2 } - 102 x - 110 ; x + \frac { 11 } { 8 }$
A) Yes
B) No

Question

Quizplus · Accepted Answer

To determine if $x - c$ is a factor of $f(x)$, we substitute $c$ into $f(x)$ and see if the result is 0. Here, $c = -\frac{11}{8}$. Substituting $x = -\frac{11}{8}$ into $f(x)$ gives: $f\left(-\frac{11}{8}\right) = 56\left(-\frac{11}{8}\right)^3 + 61\left(-\frac{11}{8}\right)^2 - 102\left(-\frac{11}{8}\right) - 110$. Simplifying this expression, if the result is 0, then $x + \frac{11}{8}$ is a factor of $f(x)$. Calculating directly or using a calculator, if $f\left(-\frac{11}{8}\right) = 0$, then $x + \frac{11}{8}$ is indeed a factor of $f(x)$.

Use the Factor Theorem to Determine Whether X - C f(x)=56x3+61x2−102x−110;x+118f ( x ) = 56 x ^ { 3 } + 61 x ^ { 2 } - 102 x - 110 ; x + \frac { 11 } { 8 }f(x)=56x3+61x2−102x−110;x+811​

Use the Factor Theorem to Determine Whether X - C $f ( x ) = 56 x ^ { 3 } + 61 x ^ { 2 } - 102 x - 110 ; x + \frac { 11 } { 8 }$