Which of the following expressions are polynomials in one variable and which are not ? State reasons for your answer. $4 x^{2}-3 x+7$.
$4 x^{2}-3 x+7$
$\Rightarrow 4 x^{2}-3 x+7 x^{0}$
$\because$ All the exponents of $x$ are whole numbers.
$\therefore $ $4 x ^{2}-3 x +7$ is a polynomial in one variable.
Check whether $-2$ and $2$ are zeroes of the polynomial $x + 2$.
Factorise : $27 x^{3}+y^{3}+z^{3}-9 x y z$
Find the zero of the polynomial : $p(x)=a x,\,\, a \neq 0$
Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=2 x^{3}+x^{2}-2 x-1$, $g(x)=x+1$.
Examine whether $x+2$ is a factor of $x^{3}+3 x^{2}+5 x+6$ and of $2 x+4$.