Verify that $x^{3}+y^{3}+z^{3}-3 x y z=\frac{1}{2}(x+y+z)\left[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}\right]$
Give possible expressions for the length and breadth of each of the following rectangles, in which their areas are given : $\boxed{\rm {Area}\,:25{a^2} - 35a + 12}$
Find the zero of the polynomial : $p(x)=a x,\,\, a \neq 0$
Find the remainder when $x^{3}+3 x^{2}+3 x+1$ is divided by $x$.
Find the value of each of the following polynomials at the indicated value of variables : $q(y)=3 y^{3}-4 y+\sqrt{11}$ at $y=2$