An engineer determines that the volume V(t)V(t)V(t) of a specialized industrial component is modeled by the polynomial:
V(t)=125t3+150t2+55t+6V(t) = 125t^3 + 150t^2 + 55t + 6V(t)=125t3+150t2+55t+6
where t t\,t is a dimension-scaling factor.
Use the factor theorem to prove that (5t+1)(5t + 1)(5t+1) is a factor of V(t)V(t)V(t).
Factorise V(t)V(t)V(t) completely.
Hence, prove that 375m3+450m2+165m+18375m^3 + 450m^2 + 165m + 18375m3+450m2+165m+18 is a multiple of 18 when m m\,m is a positive whole number.
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.