If $x+5$ is a factor of $x^{3}+13x^{2}+ax+35$,find the value of $a$.

By the Remainder Theorem,find the remainder when $p(x)$ is divided by $g(x)$,where $p(x) = x^{3} - 6x^{2} + 2x - 4$ and $g(x) = 1 - \frac{3}{2}x$.

If $p(x) = x^{2} - 2\sqrt{2}x + 1$,then $p(2\sqrt{2})$ is equal to

If $p(-3)=0,$ then one of the factors of $p(x)$ is.........

Find the following product:
$\left(\frac{x}{2}+2 y\right)\left(\frac{x^{2}}{4}-x y+4 y^{2}\right)$

Factorise $: 121 x^{2}-289 y^{2}$