If $x^{51} + 51$ is divided by $x + 1$,the remainder is

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: $x^{3}+3 x^{2} y+3 x y^{2}+y^{3}$

One of the factors of $(25 x^{2}-1)+(1+5 x)^{2}$ is

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

Find the remainder when $x^{3}+3x^{2}+3x+1$ is divided by $x+1$.