Find the value of $k$,if $x - 1$ is a factor of $p(x)$ in this case: $p(x) = kx^2 - 3x + k$.

Factorise the following: $64 m^{3} - 343 n^{3}$

Check whether the polynomial $q(t) = 4t^3 + 4t^2 - t - 1$ is a multiple of $2t + 1$.

What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
$\text{Volume} : 12ky^{2} + 8ky - 20k$

Verify whether the following are zeroes of the polynomial indicated against them:
$p(x) = 3x^2 - 1, x = -\frac{1}{\sqrt{3}}, \frac{2}{\sqrt{3}}$

Verify: $x^{3}-y^{3}=(x-y)(x^{2}+xy+y^{2})$