If $p(x) = x + 3,$ then $p(x) + p(-x)$ is equal to

If the polynomials $az^{3}+4z^{2}+3z-4$ and $z^{3}-4z+a$ leave the same remainder when divided by $z-3$,find the value of $a$.

Write whether the statement is True or False. Justify your answer.
The degree of the sum of two polynomials each of degree $5$ is always $5$.

Divide $p(x)=21+10 x+x^{2}$ by $g(x)=2+x$ and find the quotient and the remainder.

Divide $p(x) = x^{3} + 7x^{2} + 14x + 1$ by $x + 3$ and find the quotient and the remainder.

Which of the following expressions is a polynomial,and state the reason? If an expression is a polynomial,state whether it is a polynomial in one variable or not: $x^{3}+3 x^{2} y+3 x y^{2}+y^{3}$