Polynomials

In a polynomial we have many classifying categories.
In order to classify an equation we must first simplify (expand). Then from the simplified polynomial we can classify it.
Example: () – (2 + 4x-3) – ()
Simplified Polynomial: – 4x + 7
We can classify a polynomial by the number of terms or by the degree.

Classifying By the Number of Terms

The term can be a variable, a number, or the product of a number or variables. The terms can be connected by + or – signs or grouped together by brackets.

The type could be a:

1. Monomial with one term (3x)
2. Binomial with with two terms (3x – 4)
3. Trinomial with three terms ( – x + 2)
4. Polynomial with more then four terms (7ab – 6b + 8c + 7cd)

Example: + 7
# of variables: 2
# of terms: 3
Classification: Trinomial

Classifying By the Degree

The degree of a polynomial is the largest exponent on a single variable. A variable with no exponent will always have an invisible 1 as an exponent. The consent  term is the term with no variable.

Classifications:

• Constant has a degree of 0 (8)
• Linear has a degree of 1 (y – 5)
• Quadratic has a degree of 2 ( + 9)
• Cubic has a degree of 3 ()
• Quartic has a degree of 4 ($latex x^4 – 7x^2 – x)
• Quintic has a degree of 5 ()

Example: – 8
Degree: 4
Classification: Quartic
Constant Term: -8

Models