Use suitable identities to find the products : $\left(y^{2}+\frac{3}{2}\right)\left(y^{2}-\frac{3}{2}\right)$
$\left(y^{2}+\frac{3}{2}\right)\left(y^{2}-\frac{3}{2}\right)$
Using the identity $(a+b)(a-b)=a^{2}-b^{2},$ we have :
$\left(y^{2}+\frac{3}{2}\right)\left(y^{2}-\frac{3}{2}\right)=\left[y^{2}\right]^{2}-\left[\frac{3}{2}\right]^{2}=y^{4}-\frac{9}{4}$
Find the value of $k$, if $x -1$ is a factor of $p(x)$ in this case : $p(x)=2 x^{2}+k x+\sqrt{2}$
Verify whether the following are zeroes of the polynomial, indicated against them.
$p(x)=3 x+1, \,\,x=-\,\frac{1}{3}$
If $x+y+z=0,$ show that $x^{3}+y^{3}+z^{3}=3 x y z$.
Expand each of the following, using suitable identities : $(2 x-y+z)^{2}$
Find the zero of the polynomial : $p(x) = x + 5$