If $a+b+c=5$ and $a b+b c+c a=10,$ then prove that $a^{3}+b^{3}+c^{3}-3 a b c=-25.$
On dividing $p(x)=3 x^{3}-6 x^{2}+5 x-10$ by $(x-2),$ find the remainder.
Is $(x-1)$ is a factor of $3 x^{2}+7 x-10 ?$
Factorise the following:
$9 y^{2}-66 y z+121 z^{2}$
Find $p(-2)$ for the polynomial $p(x)=5 x^{2}-11 x+3$