# 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.

• A
• B
• C
• 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.

• A
• B
• C
• D

Write as the product of linear factors.

• A
• B
• C
• D

List all zeros of .

• A
• B
• C
• D

Q5:

Consider .

Write as the product of linear and irreducible quadratic factors.

• A
• B
• C
• D
• E

List all zeros of .

• A
• 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:

If is an irreducible polynomial, with , then which of the following is true?

• A or
• B .
• C is a zero divisor.
• D = either or .