Classifying Polynomials

 

Names of Polynomials by their degree

Degree

Name

Example

0

constant

5

1

linear

2x

2

quadratic

x2 + 3x + 2

3

cubic

2x3 – x2 + 3x +2

4

quartic

x4 + 2x3 – x2 + 3x + 1

5

quintic

x5 – 3x4 + x3 – 2x2 + x + 5

6

sixth degree

2x6 + 4x5 – x4 + 3x3 + 2x2 – x – 1

 

Names of polynomials by the number of terms

Number of terms

Name

Examples

1

monomial

2
3x
-3x4

2

binomial

x + 3
x3 – x2
x + y

3

trinomial

x2 + 3x + 2
x4 – x2 + 1
x2 + 2xy + y2

4 or more

polynomial

2x3 – x2 + 3x +2
x5 – 2x2 + x + 5
x2 + 2xy + y2 + 1

Examples of different types of polynomials

Name

monomial

binomial

trinomial

constant

constant monomial
3

 

 

linear

linear monomial
3x

linear binomial
3x + 2, or 3x + 2y

linear trinomial
3x + 2y + 1

quadratic

quadratic monomial
3x2

quadratic binomial
3x2 + 2

quadratic trinomial
3x2 + x + 2

cubic

cubic monomial
3x3

cubic binomial
3x3 + x

cubic trinomial
3x3 + x + 1

quartic

quartic monomial
3x4

quartic binomial
3x4 + 1

quartic trinomial
3x4 + 2x + 1

quintic

quintic monomial
3x5

quintic binomial
3x5 + 2x3

quintic trinomial
3x5 + 2x3 + 1

 

Practice:

Name each of the following polynomials by its degree and number of terms:
1) x3 + 1

2) 2x + 3y

3) x3 + x2 +x +1

4) x5 – x4

Answers
1) cubic binomial

2) linear binomial

3) cubic polynomial

4) quintic binomial

HOMEWORK ASSIGNMENT: Page 433 #14-19 and 27-34, Page 441 #25-32 and 39-42

HOMEWORK ANSWERS:

Jan 25 Alg Homework answers 001

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