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

Which of the following expressions are polynomials in one variable and which are not? State the reason for your answer. If the given expression is a polynomial,state whether it is a polynomial in one variable or not: $5 x^{2}-7 x+3 \sqrt{x}$

Factorise: $x^{3}+x^{2}-4x-4$

If $(5x - 3)^2 = 25x^2 + kx + 9$,then find $k$.

If $x+y=-4,$ then what is the value of $x^{3}+y^{3}-12xy+64?$

Factorise the expression: $x^{2}+4 y^{2}+9 z^{2}-4 x y-12 y z+6 z x$