If $x+3$ is a factor of $x^{3}+12 x^{2}+a x+60$ then $a=\ldots \ldots \ldots$
$-47$
$65$
$-65$
$47$
If $(2 x+3)(3 x-1)=6 x^{2}+k x-3,$ then find $k$.
If $a, b, c$ are all non-zero and $a+b+c=0,$ prove that $\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=3$
Factorise :
$1+64 x^{3}$
Write the coefficient of $x^{2}$ in each of the following:
$(i)$ $(x-1)(3 x-4)$
$(ii)$ $(2 x-5)\left(2 x^{2}-3 x+1\right)$
Without actually calculating the cubes, find the value of each of the following
$(21)^{3}+(15)^{3}+(-36)^{3}$
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