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2 Part 2. (Free-response Questions) i) Show all your work for each problem to obtain partial credits. (ii) Only two points should be given to a correct answer without essential work shown. (1) Let P(x) = 24 + 2x3 - x - 2 be a polynomial. (a) List all possible rational zeros of P(x) using rational zero theorem (b) Find all real zeros of P(x) using synthetic division or factoring method (c) Find all real and complex zeros if there is(are) any (d) Factor P(x) into linear and irreducible quadratic factors with real coefficients, and then factor P(x) completely into linear factors with complex coefficients (2) Compound Interest A sum of $10000 is invested at an interest rate of 6% per year. Find: (a) the amount due after 4 years when (i) compounded quarterly (ii) compounded continuously (b) the time required for the investment to double if (i) compounded monthly (ii) compounded continuously