The pressure $P\,$ in a specialized hydraulic chamber is modeled by the cubic function

P(x) = kx^3 - 11x^2 - 26x + 24

where $x\,$ represents the displacement of a control valve in millimetres and $k\,$ is a design constant.

Given that $(x + 2)$ is a factor of $P (x)$ , show that $k = 4$ .

Using algebra and showing each step of your working, fully factorise $P (x)$ .

Solve, for $0∘≤θ<360∘0^\circ \le \theta < 360^\circ$ , the equation

4\cos^3 \theta - 11\cos^2 \theta - 26\cos \theta + 24 = 0

giving your answers to one decimal place.

The pressure $P\,$ in a specialized hydraulic chamber is modeled by the cubic function

P(x) = kx^3 - 11x^2 - 26x + 24

where $x\,$ represents the displacement of a control valve in millimetres and $k\,$ is a design constant.

Given that $(x + 2)$ is a factor of $P (x)$ , show that $k = 4$ .

Using algebra and showing each step of your working, fully factorise $P (x)$ .

Solve, for $0∘≤θ<360∘0^\circ \le \theta < 360^\circ$ , the equation

4\cos^3 \theta - 11\cos^2 \theta - 26\cos \theta + 24 = 0

giving your answers to one decimal place.

1 Unit 1: Pure Mathematics A

1 Unit 1: Pure Mathematics A Questions