Write the degree of the following polynomial: $5x^{2} + 12x + 4$.

From the following polynomials,find out which of them has $(x+1)$ as a factor:
$p(x) = x^{3} - 5x^{2} + 2x + 8$

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

If $x+y=12$ and $xy=27$,find the value of $x^{3}+y^{3}$.

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 $x + 6$.

Expand the following:
$\left(4-\frac{1}{3 x}\right)^{3}$