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.
Transcript text: 8. 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
Solution Steps
Step 1: Identify the Factors
The given polynomial function is in factored form:
f(x)=(x−1−3)(x−2−3i)(x−1−3)(x−2+3i)
Step 2: Count the Factors
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.
Step 3: Determine the Degree
The polynomial has four factors:
(x−1−3)
(x−2−3i)
(x−1−3) (repeated)
(x−2+3i)
Since there are four linear factors, the degree of the polynomial is 4.