$4 x^{2}+11 x-3$ is a $\ldots \ldots$ polynomial.

The polynomial $p(x) = x^{4} - 2x^{3} + 3x^{2} - ax + 3a - 7$ when divided by $x + 1$ leaves the remainder $19$. Find the value of $a$. Also,find the remainder when $p(x)$ is divided by $x + 2$.

Expand: $(3x + 7y)(3x - 7y)$

For what value of $m$ is $x^{3}-2 m x^{2}+16$ divisible by $x+2$?

Is the following expression a polynomial? Justify your answer:
$\sqrt{3} x^{2}-2 x$

Evaluate $(555)^{2}$.