Worksheet: Polynomial Factorization into Linear and Irreducible Quadratic Factors

In this worksheet, we will practice writing polynomial functions as the product of linear and irreducible quadratic factors with real coefficients.

Q1:

Consider .

Write as the product of linear and irreducible quadratic factors.

• A
• B
• C
• D
• E

List all zeros of .

• A
• B
• C
• D

Q2:

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

Q3:

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

Q4:

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

Q5:

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

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