if (x + 8) is a factor of f(x), which of the following must be true?\nboth x = -8 and x = 8 are roots of…

if (x + 8) is a factor of f(x), which of the following must be true?\nboth x = -8 and x = 8 are roots of f(x).\nneither x = -8 nor x = 8 is a root of f(x).\nf(-8) = 0\nf(8) = 0

if (x + 8) is a factor of f(x), which of the following must be true?\nboth x = -8 and x = 8 are roots of f(x).\nneither x = -8 nor x = 8 is a root of f(x).\nf(-8) = 0\nf(8) = 0

Answer

Explanation:

Step1: Recall factor - root relationship

If $(x - a)$ is a factor of a polynomial $f(x)$, then $x=a$ is a root of $f(x)$, which means $f(a)=0$.

Step2: Identify the value of a

Given that $(x + 8)$ is a factor of $f(x)$. We can rewrite $(x + 8)$ as $(x-(-8))$. Here $a=-8$.

Step3: Determine the root

Since $(x-(-8))$ is a factor of $f(x)$, then $x=-8$ is a root of $f(x)$, so $f(-8)=0$.

Answer:

$f(-8) = 0$