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
$x^{2}+x-3+\frac{4}{x}$
Given expression $x^{2}+x-3+\frac{4}{x}$ is not a polynomial because the index of $x$ in the fourth term $\frac{4}{x}$ is $-1$
Factorise
$(x-2 y)^{3}+(2 y-3 z)^{3}+(3 z-x)^{3}$
Find the value of
$x^{3}-8 y^{3}-36 x y-216,$ when $x=2 y+6$
Write the coefficient of $x^{2}$ in the following polynomials
$\pi x^{2}-\frac{22}{7} x+3.14$
Verify whether the following are True or False:
$-3$ is a zero of $x-3$
If $x+5$ is a factor of $x^{3}+13 x^{2}+a x+35$ find the value of $a$.