Which of the following expressions are polynomials in one variable and which are not ? State reasons for your answer. $y^{2}+\sqrt{2}$
$y ^{2}+\sqrt{2}$
$\Rightarrow y ^{2}+\sqrt{2} y ^{0}$
$\because$ All the exponents of $y$ are whole numbers.
$\therefore $ $y ^{2}+\sqrt{2}$ is a polynomial in one variable.
Find the degree of the polynomials given : $2-y^{2}-y^{3}+2 y^{8}$
Find $p(0)$, $p(1)$ and $p(2)$ for of the following polynomials : $p(t)=2+t+2 t^{2}-t^{3}$
Factorise of the following : $64 a^{3}-27 b^{3}-144 a^{2} b+108 a b^{2}$
Verify that $x^{3}+y^{3}+z^{3}-3 x y z=\frac{1}{2}(x+y+z)\left[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}\right]$
Verify whether the following are zeroes of the polynomial, indicated against them.
$p(x)=2 x+1, \,\,x=\frac{1}{2}$