Without actual division, prove that $2 x^{4}-5 x^{3}+2 x^{2}-x+2$ is divisible by $x^{2}-3 x+2$

One of the factors of $\left(25 x^{2}-1\right)+(1+5 x)^{2}$ is

Expand the following:

$(3 a-2 b)^{3}$

Expand

$\left(\frac{2 x}{3}+\frac{4 y}{5}\right)\left(\frac{2 x}{3}-\frac{4 y}{5}\right)$

Check whether $p(x)$ is a multiple of $g(x)$ or not :

$p(x)=2 x^{3}-11 x^{2}-4 x+5, \quad g(x)=2 x+1$