Question

Prove by factor theorem that,
(v) $(x-3)\text{is a factor of}5x^2-21x+18$

Answer 1

To prove: $(x-3)\text{is a factor of}5x^2-21x+18$.
From Factor theorem, we know that A polynomial $f\left(x\right)$ has a factor $(x–a)$ if and only if $f\left(a\right)=0$.
$x-3=0\Rightarrow x=3$
So, $a=3$
$f\left(a\right)=f\left(3\right)$
$=5(3{)}^2-21(3)+18$
$=5\left(9\right)-21\left(3\right)+18$
$=45-63+18$
$=63-63$
$=0$
Hence, $(x-3)\text{is a factor of}5x^2-21x+18$