Factorise the following:

$16 x^{2}+4 y^{2}+9 z^{2}-16 x y-12 y z+24 x z$

Find the quotient and the remainder when $2 x^{2}-7 x-15$ is divided by

$x-2$

Factorise each of the following

$64 x^{3}+125 y^{3}+240 x^{2} y+300 x y^{2}$

Prove that $(a+b+c)^{3}-a^{3}-b^{3}-c^{3}=3(a+b)(b+c)(c+a).$

Which of the following expressions is a polynomial, state the reason ? If an expression is polynomial, state whether it is a polynomial in one variable or not

$3 x^{2}+5 x-7+\frac{8}{x}$