Expand $(3x + 5)^2$.

If $x+2a$ is a factor of $x^{5}-4a^{2}x^{3}+2x+2a+3$,find $a$.

With the help of the remainder theorem,find the remainder when the polynomial $p(x) = x^{3} + x^{2} - 26x + 24$ is divided by the divisor $x + 6$.

Write the coefficient of $x^{2}$ in the following polynomial:
$4+7x+3x^{2}$

Factorise $144 x^{2}-289 y^{2}$.

Verify whether the following is True or False:
$-3$ is a zero of $x-3$.