2. In this assignment you will evaluate the integral f f ($)dw where _$5w414w2+4$8 56335211215 f (a?) (i) Using long division Show that 232+5$+7 2 = +1+. g) x 9333323315 (ii) Let q(x) = x3 x2 a: 15. Check that q(3) = 0. This means that a: 3 is a divisor of q(rc) To verify this, use long division to nd constants a, b, c E R such that q(m) = (a: 3)(a:1:2 + ()3: + c) (iii) Explain why the 0,362 + bit: I c you found in (ii) is irreducible. (iv) Set p(m) = 2532 l 5:1: + 7. Using the method of partial fractions explained in lectures, and the factorisation of q(9:) in (ii) write 17(337 A + B$+C q(:c)_$3 a$2+b$+c for some constants A, B , C E R.