Verify whether the following are zeroes of the polynomial, indicated against them.
$p(x)=lx+m,\,\, x=-\,\frac{m}{l}$
If $x=\frac{-m}{l}$ is a zero of polynomial $p(x)=lx+m,$ then should be $0 .$
Here, $p\left(\frac{-m}{l}\right)=l\left(\frac{-m}{l}\right)+m=-m+m=0$
Therefore, $x=\frac{-m}{l}$ is a zero of the given polynomial.
Find $p(0)$, $p(1)$ and $p(2)$ for of the following polynomials : $p(x)=(x-1)(x+1)$
Verify whether the following are zeroes of the polynomial, indicated against them.
$p(x)=3 x^{2}-1,\,x=-\,\frac{1}{\sqrt{3}},\, \frac{2}{\sqrt{3}}$
Verify that $x^{3}+y^{3}+z^{3}-3 x y z=\frac{1}{2}(x+y+z)\left[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}\right]$
Factorise $8 x^{3}+27 y^{3}+36 x^{2} y+54 x y^{2}$
Find the value of $k$, if $x -1$ is a factor of $p(x)$ in this case : $p(x)=k x^{2}-\sqrt{2} x+1$