The pressure P P\,P in a specialized hydraulic chamber is modeled by the cubic function
P(x)=kx3−11x2−26x+24 P(x) = kx^3 - 11x^2 - 26x + 24 P(x)=kx3−11x2−26x+24where x x\,x represents the displacement of a control valve in millimetres and k k\,k is a design constant.
Given that (x+2)(x + 2)(x+2) is a factor of P(x)P(x)P(x), show that k=4k = 4k=4.
Using algebra and showing each step of your working, fully factorise P(x)P(x)P(x).
Solve, for 0∘≤θ<360∘0^\circ \le \theta < 360^\circ0∘≤θ<360∘, the equation
4cos3θ−11cos2θ−26cosθ+24=0 4\cos^3 \theta - 11\cos^2 \theta - 26\cos \theta + 24 = 0 4cos3θ−11cos2θ−26cosθ+24=0giving your answers to one decimal place.
