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.
What are the possible expressions for the dimensions of the cuboids whose volumes are given below?$\boxed{\rm {Volume}\,:12 k y^{2}+8 k y-20 k}$
If $x+y+z=0,$ show that $x^{3}+y^{3}+z^{3}=3 x y z$.
Verify whether the following are zeroes of the polynomial, indicated against them.
$p(x) = (x + 1) (x -2)$, $x = -\,1, \,2$
What are the possible expressions for the dimensions of the cuboids whose volumes are given below ?$\boxed{\rm {Volume}\,:3x^2-12x}$
Verify whether the following are zeroes of the polynomial, indicated against them.
$p(x)=3 x^{2}-1,\,x=-\,\frac{1}{\sqrt{3}},\, \frac{2}{\sqrt{3}}$