Download Polynomial

Introduction to
Polynomials
Learning Targets
I will be able to:
Identifying Parts Of A Monomial
Classify polynomials by the number of
terms
Classify Polynomials By Degree
IDENTIFYING PARTS OF A
MONOMIAL
Exponent
Coefficient
Variable
Let’s try an example: Identify the coefficient, variable, and
exponent:
Exponent
Coefficient
Variable
WAYS TO CLASSIFY POLYNOMIALS
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
Polynomial: 4 or more terms
Think about other words with
the prefix poly: polytheistic,
polygon
Let’s take a closer look at
classifying polynomials by number
of terms...
Polynomials
are fun!
CLASSIFYING POLYNOMIALS BY
NUMBER OF TERMS
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.
CLASSIFYING POLYNOMIALS BY
NUMBER OF TERMS
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:
CLASSIFYING POLYNOMIALS BY DEGREE
Finding the degree of a Monomial:
The sum
of the exponents of its variables.
Example 1:
Example 2:
Finding the degree of a Polynomial:
same as that of its term with the greatest degree.
Example 1:
Example 2:
The
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
The degree is 7.
B. 7ed
C. 3
Add the exponents of the
variables: 4 + 3 = 7.
Check It Out! Example 1
Find the degree of each monomial.
a. 1.5k2m
b. 4x
b. 2c3
CLASSIFYING POLYNOMIALS BY DEGREE
Finding the degree of a Polynomial:
same as that of its term with the greatest degree.
Example 1:
Example 2:
The
Some polynomials have special names based on their
degree and the number of terms they have.
Degree
Name
Terms
Name
0
Constant
1
Monomial
1
Linear
2
Binomial
2
Quadratic
Trinomial
3
4
Cubic
Quartic
3
4 or
more
5
Quintic
6 or more
6th,7th,degree and
so on
Polynomial
Example 2: Finding the Degree of a Polynomial
And its name
Find the degree of each polynomial.
A. 11x7 + 3x3
11x7: degree 7 3x3: degree 3
The degree of the polynomial is the
greatest degree, 7, so it’s 7th.
B.
The degree of the polynomial is the
greatest degree, 4, so it’s quartic.
Find the degree of
each term.
Check It Out! Example 2
Find the degree and the name of each polynomial.
a. 5x – 6
b. x3y2 + x2y3 – x4 + 2
CLASSIFYING POLYNOMIALS BY DEGREE
Degree
Name
Example
NON-EXAMPLES OF POLYNOMIALS
Fractions, Division
Square Roots
Variables as the exponent
Negatives as the exponent
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
Find the degree of each term. Then arrange them in
descending order:
6x – 7x5 + 4x2 + 9
Degree
1
5
2
–7x5 + 4x2 + 6x + 9
0
5
2
1
0
The standard form is –7x5 + 4x2 + 6x + 9. 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
Check It Out! Example 3a
Write the polynomial in standard form. Give
the leading coefficient. Then name it by
degree and number of terms.
16 – 4x2 + x5 + 9x3
Check It Out! Example 3b
Write the polynomial in standard form. Give
the leading coefficient. Then name it by
degree and number of terms.
18y5 – 3y8 + 14y
Example 4: Classifying Polynomials
Classify each polynomial according to its
degree and number of terms.
A. 5n3 + 4n
Degree 3 Terms 2
B. 4y6 – 5y3 + 2y – 9
C. –2x
5n3 + 4n is a cubic
binomial.
Classify each polynomial according to its
degree and number of terms.
D. x3 + x2 – x + 2
E. 6
F. –3y8 + 18y5 + 14y
Lesson Closing
Find the degree of each polynomial.
1. 7a3b2 – 2a4 + 4b – 15
2. 25x2 – 3x4
5
4
Write each polynomial in standard form. Then
give the leading coefficient.
3. 24g3 + 10 + 7g5 – g2 7g5 + 24g3 – g2 + 10; 7
4. 14 – x4 + 3x2
–x4 + 3x2 + 14; –1
Lesson Closing: Part II
Classify each polynomial according to its
degree and number of terms.
5. 18x2 – 12x + 5
6. 2x4 – 1
quadratic trinomial
quartic binomial