Mathematics 9709 · AS & A Level · Algebra

Algebra — practice question

The polynomial $p(x)$ has the definition $p(x) = 4x^3 + 16x^2 + 9x - 15$.
(a)[3]

Determine the quotient obtained when $p(x)$ is divided by $(2x + 3)$, and verify that the remainder equals $-6$.

(b)[2]

Evaluate $\int \frac{p(x)}{2x + 3}\,dx$.

(c)[5]

Factorise $p(x) + 6$ fully, and so solve $p(\cosec 2\theta) + 6 = 0$ for $0^\circ < \theta < 135^\circ$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Carry out the division to at least the stage $2x^2+kx$

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