factor theorem

Question 1

What does the Factor Theorem state?

Answer 1

A polynomial f(x) has a factor (x - c) if and only if f(c) = 0.

Question 2

True or False: The Factor Theorem can be used to find the roots of a polynomial.

Answer 2

True

Question 3

Fill in the blank: If f(x) is a polynomial and (x - 3) is a factor of f(x), then f(____) = 0.

Answer 3

3

Question 4

Which of the following is a consequence of the Factor Theorem? (A) All polynomials are linear. (B) Roots of a polynomial are the values that make it zero. (C) The degree of a polynomial is always positive.

Answer 4

B

Question 5

What is the first step in using the Factor Theorem to factor a polynomial?

Answer 5

Evaluate the polynomial at potential roots.

Question 6

What is the relationship between the Factor Theorem and synthetic division?

Answer 6

Synthetic division can be used to divide the polynomial by (x - c) after confirming that f(c) = 0.

Question 7

True or False: The Factor Theorem applies only to quadratic polynomials.

Answer 7

False

Question 8

Identify the polynomial: f(x) = x^3 - 6x^2 + 11x - 6. What are its roots according to the Factor Theorem?

Answer 8

1, 2, and 3

Question 9

What is an example of a polynomial that does not have (x - 4) as a factor?

Answer 9

f(x) = x^2 - 5x + 6 (since f(4) = 2 ≠ 0)

Question 10

Complete the statement: If f(x) is a polynomial and (x - r) is a factor, then r is a ____ of f(x).

Answer 10

root