Question

Find the zeroes of the polynomial $p\left(x\right)=(x-2{)}^2–(x+2{)}^2$
(2 marks)

Answer 1

Given, polynomial is $p\left(x\right)=(x-2{)}^2–(x+2{)}^2$

For zero of polynomial $p\left(x\right)=0$

$\therefore (x-2{)}^2–(x+2{)}^2=0$ (1 mark)

$\Rightarrow (x-2+x+2)(x-2-x-2)=0$

$[\text{using identity},a^2-b^2=(a-b\left)\right(a+b\left)\right]$

$\Rightarrow \left(2x\right)(-4)=0$

$\Rightarrow x=0$

Therefore, zero of the polynomial $p\left(x\right)$ is $0$. (1 mark)