Factorise
$(x-2 y)^{3}+(2 y-3 z)^{3}+(3 z-x)^{3}$
$3(x-2 y) \cdot(2 y-3 z)(3 z-x)$
By using the factor theorem, show that $(x-3)$ is a factor of the polynomial $12 x^{3}-31 x^{2}-18 x+9$ and then factorise $12 x^{3}-31 x^{2}-18 x+9$
$9 x^{2}-21 x y+10 y^{2}$
Verify whether the following are True or False:
$0$ and $2$ are the zeroes of $t^{2}-2 t.$
Find the value of each of the following polynomials at the indicated value of variables
$q(y)=5 y^{3}-4 y^{2}+14 y-\sqrt{3}$ at $y=2$
Find the value of the polynomial $3 x^{3}-4 x^{2}+7 x-5,$ when $x=-3$
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