## Precalculus (6th Edition) Blitzer

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.