(a)[5]
Find the constants $a$ and $b$.
(b)[3]
Using the values of $a$ and $b$ found in part (a), fully factorise $p(x)$.
(c)[2]
Hence determine the values of $x$ for which $p(x) < 0$.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
Let $p(x)$ stand for the polynomial $6x^3 + ax^2 + bx + 9$, where $a$ and $b$ are constants. It is stated that $(x - 3)$ is a factor of $p(x)$, and that dividing the first derivative $p'(x)$ by $(x - 3)$ leaves a remainder of $72$.