The displacement of a particle sss (in meters) from a reference point at time ttt (in seconds) is modeled by the function:
s(t)=(t−2)(3t2+10t+k)+48 s(t) = (t - 2)(3t^2 + 10t + k) + 48 s(t)=(t−2)(3t2+10t+k)+48where k k\,k is a constant.
State the remainder when s(t)s(t)s(t) is divided by (t−2)(t - 2)(t−2).
Given that the particle is at the reference point (s=0s = 0s=0) when t=23\displaystyle t = \frac{2}{3}t=32, show that k=28k = 28k=28.
Hence
fully factorise the expression for s(t)s(t)s(t),
Hence
find the number of real solutions of the equation s(t)=0s(t) = 0s(t)=0, giving a reason for your answer.
368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.