Answer
The Remainder Theorem states that if the polynomial $f\left( x \right)$ is divided by $x-c$ , then the remainder is $f\left( c \right)$.
Work Step by Step
The value of $f\left( c \right)$ is equal to the remainder when $f\left( x \right)$ is divided by $x-c$
Example:
Let us consider the dividend to be $f\left( x \right)={{x}^{2}}-3x+1$ and the divisor to be $x-2$. Use the polynomial long division method
$x-2\overset{x-1}{\overline{\left){\begin{align}
& {{x}^{2}}-3x+1 \\
& \underline{{{x}^{2}}-2x} \\
& \text{ }-x+1 \\
& \underline{\text{ }-x+2} \\
& \underline{\text{ }-1} \\
\end{align}}\right.}}$
And evaluate $f\left( c \right)$; here $c=2$ , $f\left( x \right)={{x}^{2}}-3x+1$ and one gets,
$\begin{align}
& f\left( 2 \right)={{2}^{2}}-3\cdot 2+1 \\
& =4-6+1 \\
& =-1
\end{align}$
The value of $f\left( 2 \right)$ is equal to the remainder when $f\left( x \right)={{x}^{2}}-3x+1$ is divided by $x-2$.
Thus, the remainder is $f\left( c \right)$ when $f\left( x \right)$ is divided by $x-c$.
