(i)[5]
Determine the values of $a$ and $b$.
(ii)[3]
Hence, factorise $p(x)$ fully.
(iii)[2]
State how many roots the equation $p(2^y)=0$ has, with justification.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
The polynomial $p(x)$ is given by $p(x)=ax^3+bx^2-17x-a$, where $a$ and $b$ are constants. It is also known that $(x+2)$ is a factor of $p(x)$, and that the remainder on dividing $p(x)$ by $(x-2)$ is $28$.