Q.335. - Intermediate Algebra

Question

Use the factor theorem to determine whether $x+4$ a factor of  $x^3+x^2-14x+8$.

Step-by-Step Solution

Answer

No, $x+4$ is not a factor of $x^3+x^2-14x+8$.

Step 1. Given information.

$x^3+x^2-14x+8$ and $x+4$ is the factor of polynomial function.

Step 2. To simplify the polynomial function, by using remainder theorem.

According to the remainder theorem $x+4$ is a factor of $f\left(x\right)=x^3+x^2-14x+8$ if $f\left(-4\right)=0$.

Substitute $x=-4$ in $f\left(x\right)=x^3+x^2-14x+8$.

$$\begin{gathered} f(-4)={\left(-4\right)}^3+{\left(-4\right)}^2-14\left(-4\right)+8 \\ \Rightarrow -64+16+56+8 \\ \Rightarrow -64+80 \\ \Rightarrow -16 \end{gathered}$$

Step 3. Simplified answer.

Since $f\left(-4\right)$ is not equal to zero, so $x+4$ is not a factor of $f\left(x\right)=x^3+x^2-14x+8$.