(i)[5]
Determine the values of $a$ and $b$.
(ii)[3]
With $a$ and $b$ taking these values, completely factorise $p(x)$.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
The polynomial $p(x)$ is given by $p(x) = ax^3 + bx^2 + 37x + 10$, with $a$ and $b$ as constants. You are told that $(x + 2)$ is a factor of $p(x)$. You are also told that the remainder is $40$ when $p(x)$ is divided by $(2x - 1)$.