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

Find the value of the polynomial $5x - 4x^2 + 3$ at $x = -1$.

Factorise $8 x^{3}+27 y^{3}+36 x^{2} y+54 x y^{2}$

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

Write the following cube in expanded form: $\left[x-\frac{2}{3} y\right]^{3}$

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