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1 Unit 1: Pure Mathematics A

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Question 65

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.

a.

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.

[3]
b.

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.

[4]
c.

Hence, using algebra, fully factorise A(t)A(t)A(t).

[2]
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1 Unit 1: Pure Mathematics A Questions

  1. A Level
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