Answer
The given statement is false.
Work Step by Step
We know that for a polynomial $f\left( x \right)$ divided by another polynomial $g\left( x \right)$ with quotient obtained $h\left( x \right)$ and remainder $R$, the following relation holds:
$f\left( x \right)=g\left( x \right).h\left( x \right)+R$.
Here, if $R\ne 0$, $g\left( x \right)$ can never be a factor of $f\left( x \right)$.
But when $R=0$:
$\begin{align}
& f\left( x \right)=g\left( x \right).h\left( x \right)+0 \\
& \frac{f\left( x \right)}{g\left( x \right)}=h\left( x \right)
\end{align}$
So, in this case, $g\left( x \right)$ is factor of $f\left( x \right)$.
So, the given statement is true for only one whole number $0$ but not any other whole number.
Therefore, the given statement is false.
