The pressure P P\,P in a specialized hydraulic chamber is modeled by the cubic function
P(x)=kx3−11x2−26x+24P(x) = kx^3 - 11x^2 - 26x + 24P(x)=kx3−11x2−26x+24
where 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=04\cos^3 \theta - 11\cos^2 \theta - 26\cos \theta + 24 = 04cos3θ−11cos2θ−26cosθ+24=0
giving your answers to one decimal place.
Practise Edexcel A Level Maths 1.5 Algebraic Division with exam-style questions for A Level Maths. 65 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.