The polynomial $p(x)$ has definition $p(x) = 2x^3 + 5x^2 + ax + 2a$, and $a$ is an integer.
(a)[3]
Find the quotient, in terms of $x$ and $a$, when $p(x)$ is divided by $(x + 2)$, and show that the remainder equals $4$.
(b)[6]
You are told that $\int_{-1}^{1} \frac{p(x)}{x + 2} \, dx = \frac{22}{3} + \ln b$, where $b$ is an integer. Find the values of $a$ and $b$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Carry out algebraic long division up to at least $2x^2 + kx$.” …