1. The following questions were adapted from past test and exam questions. (a) Determine the values of A, B, C and D for the equation below: [6 marks] 2x3 + 5x2 - 3x + 2 B Cx + D x(2 - 1)(x2 +1) T - x2 +1 (b) If (@-be-1)3 A (b-1c)-2 - = ab, where a, b and c / 0, find an expression for the reciprocal of A in its simplest form. [3 marks] (c) Show how (x +y)3 - (x - y) can be factorised to 2y(3x2 + y?). [Hint: You may use the factorisation (a3 - 63) = (a - b) (a2 + ab + 62)]. [3 marks] (d) A quadratic equation y = ar + br + c has only one real root, a y-intercept at y = -4, and an r-intercept at a = 2. After finding a, b and c, give the equation in the completed square form. [4 marks] (e) Given a = 37+ and b = 47, if ab = 432, find the value of x. [3 marks] (f) Show that the denominator of Va can be rationalised to V1 - x(2+ x) 2vx(1 -x) - xv1 -x x2 - 5x + 4 [3 marks]