Factorise:
$1+64 x^{3}$

Give possible expressions for the length and breadth of a rectangle whose area is given as $(20 x^{2}+22 x+6)$ square units,where $(x > 0)$.

Factorise $12 x^{3} + 17 x^{2} + 3 x - 2$.

Find the remainder obtained on dividing $p(x) = x^3 + 1$ by $x + 1$.

Factorise:
$2 x^{2}-7 x-15$

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