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Polynomials with Real and Complex Solutions

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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.

2. Find the inverse of the function f(x) = x1/3 + 2.

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.

6. If points A, B, and C lie on a coordinate line and points A and B have coordinates 15 and 7 respectively, then which of the possible coordinates for point C satisfy(ies) d(A, C) < d(B, C)?

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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.

The complex conjugate of +4i must be a root to the polynomial too.
So the polynomial has three roots: r1 = -3, r2 = +4i, r3 = -4i.
The leading coefficient a = 1.
The polynomial is

2. Find the inverse of the function f(x) = x1/3 + 2.

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