Dividing $x^{3}+125$ by $(x-5),$ the remainder is $\ldots \ldots \ldots .$

Factorise :

$2 \sqrt{2} a^{3}+8 b^{3}-27 c^{3}+18 \sqrt{2} a b c$

By acute division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: $x^{4}+1 ; x+1$

Evaluate $(132)^{2}$ by using suitable identities

Verify whether $2$ and $5$ are zeros of the polynomial $x^{2}-2 x-15$ or not.