Questions: The factored form of a polynomial function is f(x)=(x-1-sqrt(3))(x-2-3 i)(x-1-sqrt(3))(x-2+3 i). What is the degree of this function? Explain.

Solution Steps

The given polynomial function is in factored form:

\[ f(x) = (x-1-\sqrt{3})(x-2-3i)(x-1-\sqrt{3})(x-2+3i) \]

To determine the degree of the polynomial, we need to count the number of linear factors. Each factor of the form \((x-a)\) contributes a degree of 1 to the polynomial.

The polynomial has four factors:

1. \((x-1-\sqrt{3})\)
2. \((x-2-3i)\)
3. \((x-1-\sqrt{3})\) (repeated)
4. \((x-2+3i)\)

Since there are four linear factors, the degree of the polynomial is 4.

Final Answer