1. The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and + 4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.
3. If a piece of real estate purchased for $50,000 in 1998 appreciates at the rate of 5% per year, then its value t years after the purchase will be f (t) = 50,000(1.05t ) . According to this model, by how much will the value of this piece of property increase between the years 2007 and 2008?
4. Solve loga (7x +1) = loga (4x +16).
5. Find the domain of f (x) = 7 + 3x + 21 , and express it using interval notation.
Polynomials with real and complex solutions are investigated. The solution is detailed and well presented.