The vertical displacement sss (in metres) of a high-performance drone during a test maneuver is modelled by the polynomial function s(t)=2t4+pt3−8t2+qt+22s(t) = 2t^4 + pt^3 - 8t^2 + qt + 22s(t)=2t4+pt3−8t2+qt+22 where ttt represents the time in seconds after the maneuver begins, and ppp and qqq are constant coefficients.
When s(t)s(t)s(t) is divided by (t+1)(t + 1)(t+1), the remainder is 777. Show that p+q=9p + q = 9p+q=9.
When s(t)s(t)s(t) is divided by (t−2)(t - 2)(t−2), the remainder is 101010. Find the value of ppp and the value of qqq.
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.