Write the degree of each of the following polynomials

$8 x^{5}+3 x^{2}-4 x+7$

If $a, b, c$ are all non-zero and $a+b+c=0,$ prove that $\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=3$

Factorise

$x^{2}+9 y^{2}+4+6 x y+12 y+4 x$

Using suitable identity, evaluate the following:

$101 \times 102$

For the polynomial $p(x),$ if $p(7)=0,$ then $\ldots$ is………… a factor of $p(x) .$