(a)[4]
Determine the values of $a$ and $b$.
(b)[3]
Therefore factorise $p(x)$ fully.
(c)[2]
Hence solve the equation $p(3\cosec \theta) = 0$ for $90^\circ < \theta < 270^\circ$.
Mathematics 9709 · AS & A Level · Trigonometry
Trigonometry — practice question
The polynomial $p(x)$ is given by $p(x) = ax^3 + bx^2 - ax - 24$, where $a$ and $b$ are constants. It is stated that $(2x - 3)$ is a factor of $p(x)$ and that, when $p(x)$ is divided by $(x + 1)$, the remainder is $-15$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Put $x=\dfrac{3}{2}$ and set the expression equal to $0$, and put $x=-1$ and set it equal to $-15$” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI