Notes 3­1 Polynomials
Objectives:
­ Identify, evaluate, add, and subtract polynomials
­ Classify and graph polynomials
Who uses this?
Doctors can use polynomials to model blood flow. 1
­ A monomial is a number or a product of numbers and variables with whole number exponents.
Ex.
­ A polynomial is a monomial or a sum or a difference of monomials.
*each monomial in a polynomial is called a term. Polynomials:
Not polynomials:
2
­ The degree of a monomial is the sum of the exponents of the variables.
Ex. Identify the degree of a monomial.
a.
b.
c.
d. 3
­ The degree of a polynomial is given by the term with the greatest degree.
­ A polynomial is written in standard form when its terms are written in descending order by degree.
­ In standard form, the degree of the first term indicates the degree of the polynomial, and the leading coefficient is the coefficient of the first term. 4
A polynomial can be classified by its number of terms...
­ A polynomial with two terms is called a binomial
­ A polynomial with three terms is called a trinomial
­ A polynomial with 4 or more terms is called "a polynomial with x terms"
ex. polynomial with 5 terms
5
A polynomial can also be classified by its degree...
6
Ex. Rewrite each polynomial in standard form. Then identify the leading coefficient, degree, and number of terms. Name the polynomial.
a. b. 7
Ex. Rewrite each polynomial in standard form. Then identify the leading coefficient, degree, and number of terms. Name the polynomial.
a. b. 8
­ To add or subtract polynomials, combine like terms.
*Like terms are terms with the same base and exponent!
Ex. Add or subtract. Write your answer in standard form.
a. b. 9
Ex. Add or subtract. Write you answers in standard form. a.
b. 10