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.

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.
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Solution

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Solution Steps

Step 1: Identify the Factors

The given polynomial function is in factored form:

f(x)=(x13)(x23i)(x13)(x2+3i) f(x) = (x-1-\sqrt{3})(x-2-3i)(x-1-\sqrt{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 (xa)(x-a) contributes a degree of 1 to the polynomial.

Step 3: Determine the Degree

The polynomial has four factors:

  1. (x13)(x-1-\sqrt{3})
  2. (x23i)(x-2-3i)
  3. (x13)(x-1-\sqrt{3}) (repeated)
  4. (x2+3i)(x-2+3i)

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

Final Answer

The degree of the polynomial function is 4\boxed{4}.

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