May/June 2026 Paper 31

The polynomial $a{x}^3-11x^2+bx+4$, where $a$ and $b$ are constants, is denoted by $\mathrm{p}(x)$. It is given that $(x-2)$ is a factor of $\mathrm{p}(x)$, and that when ${\mathrm{p}}^{\prime }(x)$ is divided by $(x-2)$ the remainder is $24$.