Lesson Worksheet: Linear Factorization and Conjugate Root Theorems Mathematics • 10th Grade
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
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
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?