Question

Find the zeroes of the following polynomial by factorisation method: $t^3-2t^2-15t$.

Answer 1

Factorise the polynomial to find the zeroes

Given polynomial, $t^3-2t^2-15t$

First, take out the common term.

$t^3-2t^2-15t=t\left(t^2-2t-15\right)$

$=t\left(t^2-5t+3t-15\right)$ [ Splitting the middle term ]

$=t\left(t\right(t-5)+3(t-5\left)\right)$

$=t(t+3)(t-5)$

The zeroes can be found as

$t(t+3)(t-5)=0$

$\Rightarrow t=0,t+3=0,t-5=0$

$\Rightarrow t=0$, $t=-3$, $t=5$

Hence, the zeroes of the polynomial are $-3,0$ and $5$.