A theoretical model for the potential energy EEE in a micro-system is given by the function
E(t)=27t3+54t2+33t+6E(t) = 27t^3 + 54t^2 + 33t + 6E(t)=27t3+54t2+33t+6
where ttt is a dimensionless time parameter.
Use the factor theorem to prove that (3t+1)(3t + 1)(3t+1) is a factor of E(t)E(t)E(t).
Factorise E(t)E(t)E(t) completely.
Hence, prove that 108n3+216n2+132n+24108n^3 + 216n^2 + 132n + 24108n3+216n2+132n+24 is a multiple of 24 when nnn is a positive integer.
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.