Paper 2 · Calculator

Form a pair of simultaneous equations in $a$ and $b$, and show that $a = 3$ and $b = -8$.

Using $a = 3$ and $b = -8$, find the remainder when $P(x)$ is divided by $(2x + 1)$.

Factorise $P(x)$ completely into three linear factors, and solve $P(x) = 0$.