If $(x-1)$ is a factor of $x^{3}+7x^{2}+ax-3$,then find the value of $a$.

Classify the following as linear,quadratic,or cubic polynomial:
$8x^{3} - 343$

Is $x+1$ a factor of $4x^3 + 7x^2 - 2x - 5$ or not?

Factorise the following:
$4 x^{2}+20 x+25$

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 $5$.

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: $5 x^{2}-7 x+3 \sqrt{x}$