Up

Naming

We can categorize polynomials based on two characteristics that every polynomial has:  degree, and number of terms.

Definition:  The degree of a polynomial is the highest degree of any of its terms.  Remember that the degree of a term is the sum of the exponents acting on the term’s variables.

Let’s look at two charts that will help us name certain polynomials:

Degree Name
0 constant
1 linear
2 quadratic
3 cubic
4 Quartic
5 Quantic

 

 

 

 

 

 

Number of Terms Type of Polynomial
1 monomial
2 binomial
3 trinomial

 

 

 

 

To name a polynomial, simply find the name for its degree, find the name for the number of terms it has, and you’re done.  It’s that easy.  Let’s try some examples.

Example:  Name each polynomial by degree and number of terms

  1. \( - {n^3}\)
  2. \( - 5\)
  3. \(1\)
  4. \(6{x^4} + {x^3} + 9x\)

Solution:

  1. The degree is 3, and the number of terms is 1.  This is a cubic monomial.
  2. The degree is 1 (since no exponent shown means an exponent of 1) and the number of terms is 1.  So this is a constant monomial.
  3. The degree is 1 (for the same reason as in 2.) and the number of terms is 1.  Again, we have a constant monomial.
  4. The degree is 4 (highest degree on a term) and the number of terms is 3.  This is a quartic trinomial.

Below you can download some free math worksheets and practice.


Downloads:
1990 x

Name each polynomial by degree and number of terms.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Polynomials-Naming-easy

Watch below how to solve this example:

 

Downloads:
1517 x

Name each polynomial by degree and number of terms.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Polynomials-Naming-medium


Watch below how to solve this example:

 

Downloads:
1975 x

Name each polynomial by degree and number of terms.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Polynomials-Naming-hard


Watch below how to solve this example:

 
 
 

Facebook PageGoogle PlusTwitterYouTube Channel

Algebra and Pre-Algebra

Beginning Algebra
Adding and subtracting integer numbers
Dividing integer numbers
Multiplying integer numbers
Sets of numbers
Order of operations
The Distributive Property
Verbal expressions
Beginning Trigonometry
Finding angles
Finding missing sides of triangles
Finding sine, cosine, tangent
Equations
Absolute value equations
Distance, rate, time word problems
Mixture word problems
Work word problems
One step equations
Multi step equations
Exponents
Graphing exponential functions
Operations and scientific notation
Properties of exponents
Writing scientific notation
Factoring
By grouping
Common factor only
Special cases
Linear Equations and Inequalities
Plotting points
Slope
Graphing absolute value equations
Percents
Percent of change
Markup, discount, and tax
Polynomials
Adding and subtracting
Dividing
Multiplying
Naming
Quadratic Functions
Completing the square by finding the constant
Graphing
Solving equations by completing the square
Solving equations by factoring
Solving equations by taking square roots
Solving equations with The Quadratic Formula
Understanding the discriminant
Inequalities
Absolute value inequalities
Graphing Single Variable Inequalities
Radical Expressions
Adding and subtracting
Dividing
Equations
Multiplying
Simplifying single radicals
The Distance Formula
The Midpoint Formula
Rational Expressions
Adding and subtracting
Equations
Multiplying and dividing
Simplifying and excluded values
Systems of Equations and Inequalities
Graphing systems of inequalities
Solving by elimination
Solving by graphing
Solving by substitution
Word problems