c) Starting from a point O, a particle P moves due north such that its displacement (in metres) 3 from O is given by y = 40t, where t is in seconds. Also starting from O, a particle @ moves due east such that its displacement from O is given by x= t2. P y = 40t dr dt ? O x = 1 Let r be the distance between the two particles at a time t. Find the rate at which r is changing, when t = 4. d) P(x) is an even polynomial of degree 4, i.e. P(-x) = P(x). Two of its zeros are at x = 1 and x = 2. i) Find the other two roots. ii) If P(0) = 8, write P(x) in factored form. e) By using the binomial expansion, show that: 3 (q + p)" - (9- p)" = 2(1) 92-1p+2(3) qn-3p3+... What is the last term in the expansion when n is odd? What is the last term in the expansion when n is even