Answer
The Factor Theorem states that if f is a polynomial function and $f\left( c \right)=0$ , then $x-c$ is a factor of $f\left( x \right)$.
Work Step by Step
Let us take the dividend as $f\left( x \right)$ and the divisor as $x-c$; then, by the division algorithm:
$f\left( x \right)=q\left( x \right)\left( x-c \right)+r$ , where $q\left( x \right)$ is the quotient and $r$ is the remainder.
So, as per the remainder theorem, if the polynomial $f\left( x \right)$ is divided by $x-c$ , then the remainder is $f\left( c \right)$.
Now, use the remainder theorem,
$f\left( x \right)=q\left( x \right)\left( x-c \right)+f\left( c \right)$
If $f\left( c \right)=0$ , then $f\left( x \right)=q\left( x \right)\left( x-c \right)$.
Thus, this implies that $x-c$ is the factor of $f\left( x \right)$.
