The degree of 8y²z³ is 5 The degree of -10xy is 2

The degree of 8y²z³ is 5

The degree of -10xy is 2

The degree of 4 is 0 (since )

The degree of a polynomial in one variable is the same as the greatest exponent.

For example,

The degree of is 4

The degree of 3x – 4x² + 10 is 2

Examples

Find the degree of each polynomial

• 7x
• x² + 3x – 1
• 10
• 9x²y³
• 12 – 13x³ + 4x + 5x²

• 7x 1
• x² + 3x – 1 2
• 10 0
• 9x²y³ 5
• 12 – 13x³ + 4x + 5x² 3

Names of Polynomials by their Degree

Degree of 0 : Constant

For example,

7

-10

8

Degree of 1 : Linear

For example,

3x – 2

½x + 7

12x – 1

Degree of 2 : Quadratic

For example,

7x² - 3x + 6

4x² - 1

Degree of 3 : Cubic

For example,

8x³ + 5x +9

2x³ - 11

Anything with a degree of 4 or more does not have a special name 

Examples

Name each Polynomial by its degree.

• 10x³ + 2x
• 3x + 8
• 6
• 9x² + 3x – 1

5.

• 10x³ + 2x Cubic
• 3x + 8 Linear
• 6 Constant
• 9x² + 3x – 1 Quadratic

5. Not a polynomial!

Putting it all together…

Examples

Classify each polynomial based on its degree and the number of terms:

• 7x³ - 10x
• 8x – 4
• 4x² + 11x – 2
• 10x³ + 7x² + 3x – 5
• 6
• 3x² - 4x

• 7x³ - 10x cubic/binomial
• 8x – 4 linear/binomial
• 4x² + 11x – 2 quadratic/trinomial
• 10x³ + 7x² + 3x – 5 cubic/polynomial
• 6 constant/monomial
• 3x² - 4x quadratic/binomial

Standard Form

• STANDARD FORM of a polynomial means that all like terms are combined and the exponents get smaller from left to right.

Examples

Put in standard form and then name the polynomial based on its degree and number of terms.

• 4 – 6x³ – 2x + 3x²
• 3x² - 5x³ + 10 – 7x + x² + 4x

• 4 – 6x³ – 2x + 3x²

= -6x³ + 3x² – 2x + 4

cubic/polynomial

2. 3x² - 5x³ + 10 – 7x + x² + 4x

= -5x³ + 4x² – 3x + 10

cubic/polynomial

Summary

Names by Degree

• Constant
• Linear
• Quadratic
• Cubic

Names by # of Terms

• Monomial
• Binomial
• Trinomial

A word about fractions…

Coefficients and Constants can be fractions.

½x + 5 is ok!

-3x² + ½ is ok!

is not a polynomial

is not a polynomial

Assignment

Page 373

# 1 – 20

Must write problem for credit.

No partial credit if incomplete.

Summary

Copy the table and fill in the blanks.

Check yourself!