# Worksheet: Linear Factorization and Conjugate Root Theorems

In this worksheet, we will practice writing a polynomial function given its zeros using linear factorization and conjugate root theorems.

**Q1: **

Write a polynomial function of the least degree with real coefficients in standard form given that it has , and as zeros.

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**Q2: **

Write a polynomial function of least degree with real coefficients in standard form given that it has and (multiplicity 2) as zeros.

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**Q3: **

Write a polynomial function of the least degree with real coefficients in standard form given that it has , and as zeros.

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**Q5: **

Consider .

Write as the product of linear and irreducible quadratic factors.

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List all zeros of .

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**Q7: **

Consider .

Write as the product of linear and irreducible quadratic factors.

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Write as the product of linear factors.

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List all zeros of .

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**Q9: **

What is the least possible degree of a polynomial function with rational coefficients, given that it has (multiplicity 2), , and (multiplicity 3) as zeros?

**Q10: **

What is the least possible degree of a polynomial function with rational coefficients, given that it has , , and as zeros?