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…

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: Apply the Factor Theorem

The Factor Theorem states that if ((x - a)) is a factor of a polynomial (f(x)), then (f(a)=0). Here, (a = 5) since the factor is ((x - 5)).

Step2: Interpret the root

When (f(a)=0), (x=a) is a root of the polynomial (f(x)). Substituting (a = 5) into the concept of roots, if (f(5)=0), then (x = 5) is a root of (f(x)).

Answer:

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