Write the degree of each of the following polynomials

$x^{8}-6561$

Factorise

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

Find the value of the polynomial $x^{2}-7 x+12$ at.

$x=\frac{1}{2}$

Factorise the following quadratic polynomials by splitting the middle term

$x^{2}-4 x-77$

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