(a)[5]
Determine the values of $a$ and $b$.
(b)[4]
Hence, write $p(x)$ in factorised form, and determine the exact roots of the equation $p(3x) = 0$.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
The polynomial $p(x)$ is given by $p(x) = 6x^3 + ax^2 + bx - 20$, with $a$ and $b$ as constants. You are told that $(x + 2)$ is a factor of $p(x)$ and that the remainder is $-11$ when $p(x)$ is divided by $(x + 1)$.