Introduction to Polynomials

Introduction to Polynomials

by Matt Biollo

​Introduction to Polynomials

​1

​Polynomials are a combination of numbers, variables, and terms separated by addition or subtraction!

​Terms!

​

​Polynomials are split into TERMS. Terms consist of a number part, or a variable part, or both.

​

​Terms are separated by addition or subtraction!

Multiple Choice

How Many Terms are in this expression?

$$-12b+6b-4b$$  

• 1

• 2

• 3

• 4

Multiple Choice

How many terms are in the following polynomial?
_{3xy - 2y + 8x - 7z -16}

• A
  1
• B
  2
• C
  4
• D
  5

Multiple Choice

Terms in a polynomial are separated by what?

• A
  Parenthesis
• B
  Multiplication/
  Division 
• C
  Constants
• D
  Addition/
  Subtractraction

Multiple Choice

How many terms are in this polynomial?

2x³ - 8x² + 3x - 7

• 7

• 1

• 4

• 2

​Classifying Polynomials

​

​Polynomials are named based on the number of terms they have:

​Think of a "Bicycle" having 2 wheels

​

​Think of a "Tricycle" having 3 wheels

Multiple Choice

Classify by number of terms:

2x – 9

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Multiple Choice

Classify by number of terms:
12

• Monomial
• Binomial
• Trinomial
• 4-Term Polynomial

Multiple Choice

Classify by number of terms:
7x³ – 8x² + 9

• Monomial
• Binomial
• Trinomial
• 4-Term Polynomial

Multiple Choice

Classify by the number of terms

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

• Monomial
• Binomial
• Trinomial
• Polynomial

Multiple Choice

• Monomial
• Binomial
• Trinomial
• Polynomial

Multiple Choice

Classify by number of terms:
-2x² – x

• Monomial
• Binomial
• Trinomial
• 4-Term Polynomial

Multiple Choice

• Monomial
• Binomial
• Trinomial
• Polynomial

Multiple Choice

• Monomial
• Binomial
• Trinomial
• Polynomial

​Some more new vocab!

Variables

The letters in a polynomial

​

​In this case x and y are variables

Multiple Choice

What are variables in math?

• Letters

• Numbers

• Expressions

Multiple Choice

A variable is . . .

• an awesome number

• a number represented by a letter

• an infinite number

• a number multiplied by another number

Multiple Choice

5p + 4h - 2
Which are the variables? 

• 5p, 4h, 2
• 2
• p, h
• 5, 4

Multiple Choice

What are the variables in the following expression?

• 3, 4, 1 and 7
• z, x and y
• + and -
• 15

Multiple Choice

In this expression what is the variable? 
5 + y 

• q
• +
• 5
• y

Multiple Choice

What is the variable in 3x - 5

• x

• 5

• 3

Multiple Choice

What are the variables in 3x + y

• 3x

• x,y

• x

• y

Multiple Choice

Which of the following answer choices is NOT an example of a variable?

• 8
• x
• u
• n

​Some more new vocab!

​Coefficient

​Numbers in front of the variables

​

​The coefficients are multiplying the

​variables

​

​In this example, the coefficients are

​2 and 4

​Coefficients INCLUDE the sign (positive or negative) in front of the number as well.

​For example:

​

​-3x + 4. The coefficient is -3

​

2x - 3 The coefficient is 2

​

​-3x - 4y. The coefficients are -3 and -4

Multiple Choice

4 is the __________ of 4n.

• equation
• variable
• coefficient
• solution

Multiple Choice

What is the coefficient of x?
8 + 5x - y

• 8
• 0
• 5
• -5

Multiple Choice

What is the coefficient:

4 - 2y

• 2

• 4

• -2

• 0

Multiple Choice

What is the coefficient of x?

9 - 1x

• 0
• 1
• -1
• 8

Multiple Choice

What are the coefficients in the expression 8x - 3 + 12xy?

• -3, 8, 12

• x, y

• 8, 12

• There are no coefficients in this expression

Multiple Choice

Identify the coefficients in this expression. 4 + 3x + 5x

• 3x, 5x

• 4, 3x, 5x

• 3, 5

• x

​Some more new vocab!

​Constants

The numbers not attached to any

variables (they are by themselves)

​

​In this case, the constant is -9

Multiple Choice

What is the constant term in the polynomial below?
8 + 5x 

• 8
• 0
• 5
• -5

Multiple Choice

What is the constant term in the polynomial below?
 8x² + 3x - 6

• 3
• 24
• -48
• -6

Multiple Choice

What is the value of the constant?
2x² + 4x − 5

• 2
• 4
• 5
• −5

Multiple Choice

What is the constant of this polynomial?

2x³ - 8x² + 3x - 7

• 2

• -8

• 3

• -7

​Degree of a Polynomials.... Last new vocab!

​The degree is the highest exponent on a single term (you can also ADD the exponents within a single term)

​

​

Multiple Choice

2) Degree of

$$2x^2+50$$  is _____

• 50

• 2

• 4

• 1

Multiple Choice

Classify by the DEGREE:
2x² - 5

• 1
• 2
• 3
• 4

Multiple Choice

What is the highest degree among terms in this polynomial?

6x² + 7x⁴ + x3 + x

• 1

• 2

• 3

• 4

Multiple Choice

Classify by the DEGREE:
4x³ - 5x² + 2x - 1

• 1
• 2
• 3
• 4

Multiple Choice

What is the degree of the polynomial 17x + 4

• 0
• 1
• 2
• 3

Multiple Choice

What is the degree of the polynomial
 x²-2x+5

• 1
• 2
• 3
• 0

Multiple Choice

1) Degree of 2x+5 is ____________

• 2

• 1

• 5

• 4

Some mixed questions !!

​

Multiple Choice

Classify by number of terms:
3x³ – 6x

• Monomial
• Binomial
• Trinomial
• 4-Term Polynomial

Multiple Choice

Classify by number of terms:
3x² – 8x + 1

• Monomial
• Binomial
• Trinomial
• 4-Term Polynomial

Multiple Choice

Classify by number of terms:
7x³ – 8x² -4x+ 9

• Monomial
• Binomial
• Trinomial
• 4-Term Polynomial

Multiple Choice

• Monomial
• Binomial
• Trinomial
• Polynomial

Multiple Choice

• Monomial
• Binomial
• Trinomial
• Polynomial

Multiple Choice

• Monomial
• Binomial
• Trinomial
• Polynomial

Multiple Choice

Which of these has a negative leading coefficient?

• x²+9x-4
• 6x-9
• -8x+8
• 9x

Multiple Choice

The number in front of the variable is called the.... 

• exponent
• base
• coefficient
• fronter

Multiple Choice

What is the name of a polynomial with two terms?

• monomial
• binomial
• trinomial
• quadratic

Multiple Choice

What is the name of a polynomial with four or more terms?

• monomial
• binomial
• cuatromial
• polynomial

Multiple Choice

What is the coefficient of this term?

9x³

• None

• 9

• 3

• x

Multiple Choice

What is the value of the constant?
2x² + 4x − 5

• 2
• 4
• 5
• −5

Multiple Choice

A letter that represents an unknown number

• coefficient

• base

• variable

• constant

Multiple Choice

A number without a variable is called a

• Constant

• coefficient

• variable

• polynomial