Post on 31-Dec-2015
6-3 POLYNOMIALSChapter 6
OBJECTIVES
Classify polynomials and write polynomials in standard form.
Evaluate polynomial expressions.
MONOMIALS
A monomial is a number, a variable, or a product of numbers and variables with whole-number exponents.
The degree of a monomial is the sum of the exponents of the variables. A constant has degree 0.
EXAMPLE 1: FINDING THE DEGREE OF A MONOMIAL
Find the degree of each monomial. A. 4p4q3
Sol: The degree is 7 Add the exponents of the variables: 4 + 3 = 7.
B. 7ed The degree is 2. Add the exponents of the
variables: 1+ 1 = 2. C. 3 Sol:The degree is 0.
CHECK IT OUT ! EXAMPLES
Find the degree of each monomial. A. 1.5k2m B. 4x C. 2c3
D.3yxz
POLYNOMIALS
A polynomial is a monomial or a sum or difference of monomials.
The degree of a polynomial is the degree of the term with the greatest degree.
EXAMPLE 2: FINDING THE DEGREE OF A POLYNOMIAL
Find the degree of each polynomial. A. 11x7 + 3x3
Sol:
11x7: degree 7 3x3: degree 3 The degree of the polynomial is the greatest
degree, 7.
The degree of the polynomial is the greatest degree, 4.
B.
CHECK IT OUT ! EXAMPLE
A. x3y2 + x2y3 – x4 + 2 Sol: The degree of the polynomial is the
greatest degree, 5.
STANDARD FORM OF A POLYNOMIAL
The terms of a polynomial may be written in any order. However, polynomials that contain only one variable are usually written in standard form.
The standard form of a polynomial that contains one variable is written with the terms in order from greatest degree to least degree. When written in standard form, the coefficient of the first term is called the leading coefficient.
EXAMPLE 3A: WRITING POLYNOMIALS IN STANDARD FORM
Write the polynomial in standard form. Then give the leading coefficient.
6x – 7x5 + 4x2 + 9 Sol: Find the degree of each term. Then arrange
them in descending order:
6x – 7x5 + 4x2 + 9 –7x5 + 4x2 + 6x + 9
Degree 1 5 2 0 5 2 1 0–7x5 + 4x2 + 6x + 9.The standard form is The leading
coefficient is –7.
EXAMPLE 3B: WRITING POLYNOMIALS IN STANDARD FORM
Write the polynomial in standard form. Then give the leading coefficient.
y2 + y6 – 3y Sol: Find the degree of each term. Then arrange
them in descending order:y2 + y6 – 3y y6 + y2 – 3y
Degree 2 6 1 2 16The standard form is The leading coefficient is 1.
y6 + y2 – 3y.
CHECK IT OUT! EXAMPLE
Write the polynomial in standard form. Then give the leading coefficient.
16 – 4x2 + x5 + 9x3
POLYNOMIALS
Some polynomials have special names based on their degree and the number of terms they have. Degree Name
0
1
2
Constant
Linear
Quadratic
3
4
5
6 or more 6th,7th,degree and so on
Cubic
Quartic
Quintic
NameTerms
Monomial
Binomial
Trinomial
Polynomial4 or more
1
2
3
EXAMPLE 4: CLASSIFYING POLYNOMIALS
Classify each polynomial according to its degree and number of terms.
A. 5n3 + 4n Degree 3 Terms 2 5n3 + 4n is a cubic binomial. B. 4y6 – 5y3 + 2y – 9 Degree 6 Terms 4
C. –2x Degree 1 Terms 1 –2x is a linear monomial.
4y6 – 5y3 + 2y – 9 is a
6th-degree polynomial.
CHECK IT OUT!
Classify each polynomial according to its degree and number of terms.
b. 6 c. –3y8 + 18y5 + 14y
a. x3 + x2 – x + 2
APPLICATION
A tourist accidentally drops her lip balm off the Golden Gate Bridge. The bridge is 220 feet from the water of the bay. The height of the lip balm is given by the polynomial –16t2 + 220, where t is time in seconds. How far above the water will the lip balm be after 3 seconds?
Sol: After 3 seconds the lip balm will be 76 feet
from the water.
STUDENT GUIDED PRACTICE
DO even problems from 4-21 in your book page 409
HOMEWORK
Do even problems 27-42 in your book page 409
CLOSURE
Today we learned about polynomials Next class we are going o learn about
adding and subtracting polynomials