The altitude A(t)A(t)A(t) of a research drone relative to its launch platform is modeled by the function A(t)=3t3+pt2+qt−20A(t) = 3t^3 + pt^2 + qt - 20A(t)=3t3+pt2+qt−20 for t≥0t \ge 0t≥0, where ppp and qqq are constants.
Given that (3t−2)(3t - 2)(3t−2) is a factor of A(t)A(t)A(t), show that 2p+3q=862p + 3q = 862p+3q=86.
Given further that when A(t)A(t)A(t) is divided by (t+1)(t + 1)(t+1), the remainder is q−36q - 36q−36, find the value of ppp and the value of qqq.
Hence, using algebra, fully factorise A(t)A(t)A(t).
Practise Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 226 questions covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division, 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.
