Find the quotient and the remainder when $2 x^{2}-7 x-15$ is divided by
$x+1$
Quotient $=2 x-9,$ Remainder $=-6$
Without finding the cubes, factorise
$(x-2 y)^{3}+(2 y-3 z)^{3}+(3 z-x)^{3}$
By remainder Theorem find the remainder, when $p(x)$ is divided by $g(x),$ where
$p(x)=4 x^{3}-12 x^{2}+14 x-3, g(x)=2 x-1$
If $x-2$ is a factor of $x^{3}-3 x^{2}+a x+24$ then $a=\ldots \ldots \ldots$
If $x^{2}-8 x-20=(x+a)(x+b),$ then $a b=\ldots \ldots \ldots$
On dividing $x^{3}+a x^{2}+19 x+20$ by $(x+3),$ if the remainder is $a,$ then find the value of $a$.
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