Determine which of the following polynomials has $x-2$ a factor :

$3 x^{2}+6 x-24$

$4 x^{2}+ x-2$

Expand

$(2 x-y-5)^{2}$

If $a+b+c=5$ and $a b+b c+c a=10,$ then prove that $a^{3}+b^{3}+c^{3}-3 a b c=-25.$

The following expressions are polynomials? Justify your answer:

$\frac{1}{5 x^{-2}}+5 x+7$

Factorise :

$a^{3}-2 \sqrt{2} b^{3}$