$4x^{2} - 20x + 25 = (\ldots \ldots \ldots)^{2}$

By Remainder Theorem,find the remainder when $p(x)$ is divided by $g(x)$,where $p(x) = x^{3} - 2x^{2} - 4x - 1$ and $g(x) = x + 1$.

Evaluate the following using suitable identities: $(105)^{3}$

Which of the following expressions are polynomials in one variable and which are not? State reason for your answer. If the given expression is a polynomial,state whether it is a polynomial in one variable or not: $x^{2}-8x+15$

If $x-2$ is a factor of $x^{3}-3x^{2}+ax+24$,then $a = \ldots$

If $49 x^{2}-b=\left(7 x+\frac{1}{2}\right)\left(7 x-\frac{1}{2}\right),$ then the value of $b$ is