Polynomials

Question 1

What is a polynomial?

Answer 1

A polynomial is an algebraic expression that consists of variables, coefficients, and non-negative integer exponents.

Question 2

True or False: A polynomial can have negative exponents.

Answer 2

False

Question 3

What is the degree of the polynomial 4x^3 + 2x^2 - x + 7?

Answer 3

3

Question 4

Fill in the blank: The polynomial 5x^4 - 3x^2 + 2 can be classified as a ______ polynomial.

Answer 4

quartic

Question 5

What is the leading coefficient of the polynomial 6x^5 - 4x^3 + x?

Answer 5

6

Question 6

Which of the following is a polynomial: 3x^2 + 2x - 5, 1/x + 2, or sqrt(x)?

Answer 6

3x^2 + 2x - 5

Question 7

True or False: The expression x^2 + 2x + 1 can be factored as (x + 1)(x + 1).

Answer 7

True

Question 8

What is the sum of the polynomials (2x^2 + 3x) and (4x^2 - x + 1)?

Answer 8

6x^2 + 2x + 1

Question 9

Which term is the constant term in the polynomial 7x^3 + 4x^2 - 2x + 5?

Answer 9

5

Question 10

Fill in the blank: The polynomial expression 2x^3 - 3x + 1 is of degree ______.

Answer 10

3

Question 11

What is the product of the polynomials (x + 2) and (x - 3)?

Answer 11

x^2 - x - 6

Question 12

True or False: The polynomial x^4 - 5x^2 + 6 can be factored into linear factors.

Answer 12

False

Question 13

What is the difference of the polynomials (3x^3 + 2x) and (x^3 - 4x)?

Answer 13

2x^3 + 6x

Question 14

What is the value of the polynomial 2x^2 - 3x + 4 when x = 2?

Answer 14

6

Question 15

Fill in the blank: A polynomial with one term is called a ______ polynomial.

Answer 15

monomial

Question 16

What is the result of dividing the polynomial 4x^4 by 2x^2?

Answer 16

2x^2

Question 17

Which of the following is the correct factorization of x^2 - 9?

Answer 17

(x - 3)(x + 3)

Question 18

True or False: The polynomial 5x^3 + 4x^2 - x + 10 is a cubic polynomial.

Answer 18

True

Question 19

What is the remainder when the polynomial 3x^3 + 2x^2 - x + 5 is divided by x - 1?

Answer 19

9

Question 20

Fill in the blank: The polynomial 4x^2 + 7x + 10 can be classified as a ______ polynomial.

Answer 20

quadratic

Question 21

What is the zero of the polynomial x^2 - 4?

Answer 21

x = 2 or x = -2

Question 22

What is the leading term of the polynomial 9x^5 - 3x^4 + 2x?

Answer 22

9x^5

Question 23

True or False: The polynomial 3x^2 - 2x + 1 has a maximum value.

Answer 23

False

Question 24

What is the result of evaluating the polynomial 2x^2 + 3 at x = -1?

Answer 24

5

Question 25

Fill in the blank: The polynomial x^3 + 2x^2 + x can be expressed as ______.

Answer 25

x(x^2 + 2x + 1)