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).
302 exam-style questions on WJEC A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Algebra and Functions, 1.2.2 Algebra and Functions, 1.2.3 Algebra and Functions, 1.2.4 Algebra and Functions, 1.2.5 Algebra and Functions, 1.2.6 Algebra and Functions, 1.2.7 Algebra and Functions, 1.2.8 Algebra and Functions, 1.2.9 Algebra and Functions, 1.2.10 Algebra and Functions, 1.2.11 Algebra and Functions, and 1.2.12 Algebra and Functions. Each one has a worked solution and a mark scheme showing where the marks go.