(i)[4]
Determine the value of $a$ and then factorise $p(x)$.
(ii)[5]
For the value of $a$ found in part (i), write $\frac{8x - 13}{p(x)}$ in partial fractions.
Mathematics 9709 · AS & A Level · Algebra
Algebra — practice question
The polynomial $p(x)$ is given by $p(x) = ax^3 - x^2 + 4x - a$, where $a$ is a constant. You are told that $(2x - 1)$ divides $p(x)$ exactly.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use $x=\tfrac12$, or divide by $(2x-1)$, to obtain the quadratic and set the remainder equal to zero” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI