The fuel consumption rate S(t)S(t)S(t) (in kg/s) of a prototype hypersonic engine, where ttt is the time in minutes since ignition, is modelled by the polynomial S(t)=2t3+Pt2+Qt−20S(t) = 2t^3 + Pt^2 + Qt - 20S(t)=2t3+Pt2+Qt−20, where PPP and QQQ are constants.
It is given that:
Show that P−2Q=3P - 2Q = 3P−2Q=3.
Given also that (2t−5)(2t - 5)(2t−5) is a factor of S(t)S(t)S(t),
Find the value of PPP and the value of QQQ.
Hence find the quadratic expression g(t)g(t)g(t) such that S(t)=(2t−5)g(t)S(t) = (2t - 5)g(t)S(t)=(2t−5)g(t).
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.