(i)[5]
Find $a$ and $b$.
(ii)[4]
Once $a$ and $b$ have these values, check that $(x - 2)$ is a factor of $p(x)$ and then factorise $p(x)$ fully.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
Let $p(x)$ denote the polynomial $2x^3 + ax^2 + bx + 6$, where $a$ and $b$ are constants. It is stated that dividing $p(x)$ by $(x - 3)$ leaves a remainder of $30$, and dividing $p(x)$ by $(x + 1)$ leaves a remainder of $18$.