The polynomial $p(x)$ is given by $p(x) = 2x^3 + 3x^2 + kx - 30$, with $k$ as a constant. You are told that $(x - 3)$ is a factor of $p(x)$.
(a)[2]
Find the value of $k$ from the factor information.
(b)[3]
Hence find the quotient on dividing $p(x)$ by $(x - 3)$ and write $p(x)$ in completely factorised form.
(c)[3]
You are told that $a$ is one of the roots of the equation $p(x) = 0$. You are also told that $|4y - 5| = a$ has two real solutions. Find these two values of $y$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute $x=3$, set it equal to zero and try to solve” …