18 7. (i) The polynomial F(x) is a quartic such that F(x) = px 4 + qx 3 + 2x 2 + rx + s where p, q, r and s are distinct constants. Determine the number of possible quartics given that (a) the constants p, q, r and s belong to the set {– 4, –2, 1, 3, 5} (1) (b) the constants p, q, r and s belong to the set {– 4, –2, 0, 1, 3, 5} (1) (ii) A 3-digit positive integer N = abc has the following properties • N is divisible by 11 • the sum of the digits of N is even • N ≡ 8 mod 9 (a) Use the first two properties to show that a – b + c = 0 (2) (b) Hence determine all possible integers N, showing all your working and reasoning. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________