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

Factorise $y^2 - 5y + 6$ by using the Factor Theorem.

Find the value of the following polynomial at the indicated value of the variable: $p(t) = 4t^4 + 5t^3 - t^2 + 6$ at $t = a$.

Factorise each of the following: $27 p^{3} - \frac{1}{216} - \frac{9}{2} p^{2} + \frac{1}{4} p$

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

Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases: $p(x) = 2x^3 + x^2 - 2x - 1$,$g(x) = x + 1$.