Algebra Seminar Introduction to Polynomials

I DENTIFYING P ARTS O F A M ONOMIAL Coefficient Variable Exponent Let’s try an example: Identify the coefficient, variable, and exponent: Coefficient Variable Exponent

W AYS TO C LASSIFY P OLYNOMIALS We can classify polynomials by the number of terms: Monomial: 1 term Think about other words with the prefix mono : monotone, monochromatic, monologue Binomial: 2 terms Think about other words with the prefix bi : bicycle, bifocals, bimonthly Trinomial: 3 terms Think about other words with the prefix tri : tricycle, triathlon, triceratops OR by the degree of the polynomial...More on this later... Let’s take a closer look at classifying polynomials by number of terms... Polynomials are fun!

C LASSIFYING P OLYNOMIALS B Y N UMBER O F T ERMS Monomial: a number, a variable, or the product of a number and one or more variables. We are also going to call this a term. Let’s check out some examples of monomials: A monomial with no variables is called a constant.

C LASSIFYING P OLYNOMIALS B Y N UMBER O F T ERMS Binomial: a polynomial with 2 terms Let’s check out some examples of binomials: Trinomial: a polynomial with 3 terms Let’s check out some examples of trinomials:

C LASSIFYING P OLYNOMIALS B Y D EGREE Finding the degree of a Monomial : The sum of the exponents of its variables. Example 1: Finding the degree of a Polynomial : The same as that of its term with the greatest degree. Example 1: Example 2:

C LASSIFYING P OLYNOMIALS B Y D EGREE DegreeNameExample

N ON -E XAMPLES OF P OLYNOMIALS Fractions, Division Square Roots Variables as the exponent Negatives as the exponent Remember... these are NOT polynomials!