Question

Check whether $x+3$ is a factor of $p\left(x\right)=x^2-9$.

Answer 1

Step 1. Find zero of $x+3$:

Here, the polynomial $p\left(x\right)=x^2-9$.

For finding zero,

$x+3=0$

$\Rightarrow x=-3$

Therefore, $-3$ is a zero of $x+3$.

Step 2. Find $x=-3$ is a zero of $p\left(x\right)=x^2-9$ or not:

If any real number $a$ is a root or zero of a polynomial $p\left(x\right)$ if and only if $p\left(a\right)=0$.

On substituting $x=-3$ in $p\left(x\right)=x^2-9$,

$\begin{array}{rcl}p(-3)& =& {(-3)}^2-9\\ & =& 9-9\\ & =& 0\end{array}$

Therefore, $x=-3$ is a zero of polynomial $p\left(x\right)=x^2-9$.

Hence, $x+3$ is a factor of $p\left(x\right)=x^2-9$.