(a)[5]
Find values of $a$ and $b$.
(b)[3]
Hence factorise $p(x)$ and show that the equation $p(x) = 0$ has one, and only one, real root.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
The polynomial $p(x)$ is given by $p(x) = ax^3 - ax^2 + ax + b$, with $a$ and $b$ as constants. You are told that $(x + 2)$ is a factor of $p(x)$, and that the remainder is $35$ when $p(x)$ is divided by $(x - 3)$.