Classifying Polynomials

Intro to Polynomials

What is a polynomial?

A polynomial is an algebraic expression made up of terms connected by operations of adding or subtracting (plus and/or minus)

For example: 5ab + 4a² - 10bc

In expressions, terms are separated by + or - signs

A binomial has two terms, separated by a plus or minus.
ex: 7x + 3y
8a - 2b
-3abc - 4def

Binomial

A monomial has one term.

ex: 5, 7x, -3y, 10pqr

Monomial

Types of polynomials

Any algebraic expression with 4 or more terms, we just generally call a polynomial
ex: 7w + 8x - 9y + z
5x³ - 7x² - 9x + 4

Polynomial

A trinomial has three terms.

ex: 4x² + 5x - 6
-5a + 4b - c
8j - 2k + 4jk²

Trinomial

Types of polynomials

YOUR TURN

Answer the following questions about polynomials

Multiple Choice

How many terms does the following expression have?

2x + 4xy + 5y - 3

• 1

• 2

• 3

• 4

Multiple Choice

How many terms does the following expression have?

9xyz

• 1

• 2

• 3

• 4

Multiple Choice

How many terms does the following expression have?

5rt - rt²

• 1

• 2

• 3

• 4

Multiple Choice

How many terms does the following expression have?

-3m + 4mn - 8n

• 1

• 2

• 3

• 4

Multiple Choice

How many terms does the following expression have?

2x + 3y

• 1

• 2

• 3

• 4

Multiple Choice

What is the name of this type of polynomial?

6x

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

What is the name of this type of polynomial?

x + y + 4

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

What is the name of this type of polynomial?

x³ + 4x² -5x + 3

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

What is the name of this type of polynomial?

8

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

What is the name of this type of polynomial?

2x² + 3y²

• Monomial

• Binomial

• Trinomial

• Polynomial

Algebra and
Polynomial Vocabulary

​The number in front of a variable​.

In the above example, 5 and 2 are coefficients.

Coefficient

Letters in our algebraic expression. They represent an unknown number.

In the above example, x and y are variables

Variable

A number that does not have a variable with it.

In the above example, -7 is a constant

Constant

The largest exponent in an algebraic expression.

In the above example, the polynomial has a degree of 2 (because x² is the largest exponent)

Degree

In a monomial, the degree is the sum of the exponents of the variables.
Remember: If the variable has no exponent, the exponent is 1.

Degree of a monomial

YOUR TURN

Answer the following questions about polynomials

Multiple Choice

What is the DEGREE of the polynomial 3x³ + 2x⁴ + 5x ?

• 1

• 2

• 3

• 4

Multiple Choice

What is the DEGREE of the polynomial 17x + 4

• 0

• 1

• 2

• 3

Multiple Choice

What is the constant term in this polynomial?

2x³ - 8x² + 3x - 7

• 2

• -8

• 3

• -7

Multiple Select

What are the coefficients in: 2x³ - 4x² + 6x - 5

• 2

• 3

• -4

• 6

• -5

Multiple Choice

What is the degree of this monomial?
-7xyz²

• 3
• 4
• -7
• 7

Multiple Choice

What is the degree of 12qrst⁵

• 8

• 9

• 10

• 11

• 12

Multiple Choice

What is the constant in the polynomial?
-2xyz + 3x² - 2y² - 6z² + 32

• -2
• 3
• -6
• 32

Multiple Select

What is/are the variable(s) in: 2x³ - 5x² + 6x - 3

• x

• x²

• x³

Multiple Choice

What is the coefficient of: x²y³z⁴

• 1

• 2

• 3

• 4

• There isn't one

Multiple Choice

REVIEW: How many terms are in this expression:

9x⁴ + 3x³ -7x² - 8x - 18

• 3

• 4

• 5

• 6

Open Ended

Reflect: What is something that you learned in today's lesson?

Poll

Reflect: How do you feel after today's lesson?

• I didn't get anything!

• I feel confused. I have questions

• I feel so-so. I am starting to understand

• I get it. I am feeling good

• I get it completely. I feel like an expert