if (x - 5) is a factor of f(x), which of the following must be true?\na root of f(x) is x = -5.\na root of…

if (x - 5) is a factor of f(x), which of the following must be true?\na root of f(x) is x = -5.\na root of f(x) is x = 5.\nboth x = -5 and x = 5 are roots of f(x).\nneither x = -5 nor x = 5 is a root of f(x).

if (x - 5) is a factor of f(x), which of the following must be true?\na root of f(x) is x = -5.\na root of f(x) is x = 5.\nboth x = -5 and x = 5 are roots of f(x).\nneither x = -5 nor x = 5 is a root of f(x).

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 $f(x)$.

Step2: Identify the root

Given $(x - 5)$ is a factor of $f(x)$, by the factor - root relationship, when $x = 5$, $f(5)=0$. So $x = 5$ is a root of $f(x)$.

Answer:

B. A root of $f(x)$ is $x = 5$.