Question

Using the factor theorem, verify that $x+5$ is a factor of $f\left(x\right)=x^2+9x+20$.

Answer 1

The factor theorem states that a polynomial $f\left(x\right)$ has a factor $(x-k)$ if and only if $f\left(k\right)=0$. If $x+5$ is a factor, then $x=-5$ is a root.
To verify the root, substitute $x=-5$ in $f\left(x\right)=0$.
$f(-5)=x^2+9x+20$
$0=(-5{)}^2+9(-5)+20$
$0=25-45+20$
$0=0$
Therefore, the given factor $(x+5)$ is a factor of $x^2+9x+20$.