# Lesson Worksheet: Linear Factorization and Conjugate Root Theorems Mathematics

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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• B
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• D
• E

Q2:

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

• A
• B
• C
• D

Q3:

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

• A
• B
• C
• D
• E

Q4:

Consider .

Write as the product of linear and irreducible quadratic factors.

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• B
• C
• D

Write as the product of linear factors.

• A
• B
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• D

List all zeros of .

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• B
• C
• D

Q5:

Consider .

Write as the product of linear and irreducible quadratic factors.

• A
• B
• C
• D
• E

List all zeros of .

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• B
• C
• D
• E

Q6:

Consider .

Write as the product of linear and irreducible quadratic factors.

• A
• B
• C
• D
• E

List all zeros of .

• A
• B
• C
• D

Q7:

Consider .

Write as the product of linear and irreducible quadratic factors.

• A
• B
• C
• D
• E

Write as the product of linear factors.

• A
• B
• C
• D
• E

List all zeros of .

• A
• B
• C
• D

Q8:

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

Q9:

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

This lesson includes 2 additional questions and 18 additional question variations for subscribers.