Question

The factors when $x^3-9x^2+24x-20$ is factorised using Rational Root Theorem, are

Answer 1

$f\left(x\right)=x^3-9x^2+24x-20$
By Rational Root Theorem, Possible roots will be $\frac{p}{q}$, where $p$ is a factor of constant term $20$ and $q$ is a factor of leading coefficient $1$.
Possible rational zeroes are $\pm 1,\pm 2,\pm 4,\pm 5,\pm 10,\pm 20$
putting $x=2$, we get $f\left(2\right)=0$
$\therefore (x-2)$ is a factor of $f\left(x\right)$
Now,
$x^3-9x^2+24x-20=(x-2)(x^2-7x+10)$
$=(x-2)(x-2)(x-5)$
$\therefore$ The factors are $(x-2)$ and $(x-5)$.