Adding and Subtracting Polynomials

Question 1

What is a polynomial?

Answer 1

A polynomial is an algebraic expression that consists of variables raised to non-negative integer powers and coefficients.

Question 2

True or False: The degree of a polynomial is determined by the highest power of its variable.

Answer 2

True

Question 3

Fill in the blank: When adding polynomials, you combine like terms, which are terms that have the same ________.

Answer 3

variable and exponent

Question 4

What is the first step in adding two polynomials?

Answer 4

Identify and group the like terms.

Question 5

When subtracting polynomials, what must you remember to do with the second polynomial?

Answer 5

Distribute the negative sign to all terms in the second polynomial.

Question 6

Multiple choice: Which of the following is a polynomial? A) 3x^2 + 2x - 1 B) 4/x + 2 C) √x + 7

Answer 6

A) 3x^2 + 2x - 1

Question 7

What is the result of adding (2x^2 + 3x) and (4x^2 + 5)?

Answer 7

6x^2 + 3x + 5

Question 8

True or False: You can only add polynomials that have the same degree.

Answer 8

False

Question 9

What is the term for the coefficient of the highest degree term in a polynomial?

Answer 9

Leading coefficient

Question 10

Fill in the blank: The sum of a polynomial and its opposite is ________.

Answer 10

zero

Question 11

What do you call the process of combining like terms in a polynomial?

Answer 11

Simplification

Question 12

Multiple choice: Which operation requires distributing a negative sign? A) Addition B) Subtraction C) Multiplication

Answer 12

B) Subtraction

Question 13

What is the result of subtracting (x^3 + 2x) from (4x^3 + 3)?

Answer 13

3x^3 - 2x + 3

Question 14

True or False: The order of addition of polynomials does not affect the result.

Answer 14

True

Question 15

What do you call the terms in a polynomial that do not have a variable?

Answer 15

Constant terms

Question 16

Fill in the blank: The degree of the polynomial 5x^4 + 2x^3 - x + 7 is ________.

Answer 16

4

Question 17

What is the sum of the polynomials (3x^2 - x + 4) and (-2x^2 + 3x - 5)?

Answer 17

x^2 + 2x - 1

Question 18

Multiple choice: When adding (3x + 2) and (2x + 5), the resulting constant term is: A) 2 B) 5 C) 7

Answer 18

C) 7

Question 19

What happens to the degree of a polynomial when you add a lower degree polynomial to it?

Answer 19

The degree remains the same as the higher degree polynomial.

Question 20

True or False: When subtracting polynomials, the like terms must be in the same order.

Answer 20

False

Question 21

What is the leading term of the polynomial 6x^5 - 4x^3 + 2?

Answer 21

6x^5

Question 22

Fill in the blank: The result of adding a polynomial to zero is ________.

Answer 22

the polynomial itself

Question 23

What is the difference between a monomial and a polynomial?

Answer 23

A monomial is a polynomial with only one term.

Question 24

Multiple choice: Which of the following operations can be performed on polynomials? A) Addition B) Subtraction C) Both A and B

Answer 24

C) Both A and B

Question 25

What is the effect of adding a polynomial and its inverse?

Answer 25

The result is zero.

Question 26

True or False: The coefficients of like terms must be added together when combining polynomials.

Answer 26

True

Question 27

How can you quickly determine the correct interval for this function?

Answer 27

The parabolic function must be symmetrical about the vertex; moreover, the f(a) and f(b) must have equal outputs.