Question

Show that $a-3$ is a factor of $a^3-3a^2+4a-12$

Answer 1

Let $p\left(a\right)=$ $a^3-3a^2+4a-12$
By the factor theroem, $a-3$ is a factor of $p\left(a\right)$, if $p\left(3\right)=0$
Find the value of $p\left(3\right)$
$p\left(3\right)=a^3-3a^2+4a-12$ ......(Substitute $a=3$)
$p\left(3\right)=3^3-3(3{)}^2+4(3)-12$
$0=27-27+12-12$
$0=0$
Therefore, $a-3$ is a factor of $p\left(a\right)$.