Chapter 3-1 Polynomials
Obj: SWBAT identify, evaluate, add, and subtract polynomials
A monomial – is a number, a variable, or a product of numbers and variables
with whole number exponents
Examples:
A polynomial - is a monomial or a sum or difference of monomials
(polynomials have no variables in denominators, no roots or absolute values
of variables, and all variables have whole number exponents)
Determine if the following are Polynomials – yes or no…explain
3𝑥 4
1
√𝑥
2
3𝑥 − 7
8
𝑥 2 + 3𝑥 − 7
5𝑦 2
1
2𝑧12 + 9𝑧 3
2
𝑎7
𝑚3.73 + 𝑚−2
Degree of a monomial – is the sum of the exponents of the variables (and
only the variables!!)
Identify the degree of the following monomials
𝑎) 𝑥 4
𝑏) 𝑎2 𝑏 4
𝑐) 12
𝑑) 42 𝑥 2 𝑦 7 𝑧
Degree of a Polynomial – is determined by the term with the greatest degree
𝑎) 𝑥 2 + 7𝑥 4 − 5
𝑏) 6 + 2𝑥 − 4𝑥 7 + 3𝑥 5
Standard Form – a polynomial with one variable is in “Standard Form” when
its terms are written in descending order by degree.
Degree of Polynomial
5𝑥 3 + 8𝑥 2 + 3𝑥 − 17
Ex
3
Leading
Coefficient
2
1
0
Degree of each term
Classifying Polynomials – By Number of Terms and By Degree
Polynomials classified by the number of terms:
Monomial  one term
Binomial

Trinomial 
________  ___________
Polynomials classified by degree
Name
Degree
Constant
0
Linear
1
Quadratic
2
Cubic
3
Quartic
4
Quintic
5
Example
Classify the following polynomials – Rewrite into Standard Form, Identify the
Leading Coefficient, Then classify by the Degree and Number of Terms
𝑎) 2𝑥 + 4𝑥 3 − 1
𝑏) 7𝑥 3 − 11𝑥 + 𝑥 5 − 2
𝑐) 𝑥 2 − 7
𝑑) 4 − 9𝑥 2 + 3𝑥 − 12𝑥 3 + 7𝑥 2
Adding and Subtracting Polynomials –
Add or subtract, write answer in Standard Form
𝑎) (3𝑥 2 + 7𝑥 + 𝑥 ) + (14𝑥 3 + 2 + 𝑥 2 − 𝑥)
𝑏) (−36𝑥 2 + 6𝑥 − 11) + (6𝑥 + 16𝑥 3 − 5)
𝑐) (5𝑥 3 + 12 + 6𝑥 2 ) − (15𝑥 2 + 3𝑥 − 2)
𝑑) (−4𝑥 + 5𝑥 2 ) − (−4𝑥 − 5𝑥 2 + 7)
Sum –up
What is a monomial? A Polynomial? Name some TYPES of Polynomials
How do we determine the degree of a Monomial?....Of a Polynomial?
Re-write in Standard Form:
𝑎) 3 − 𝑥 3 + 2𝑥 2
𝑏) − 3𝑥 2 + 2𝑥 4 + 12𝑥 − 𝑥 5 + 2
What is the leading coefficient, degree from above …classify the polynomial by
degree and number of terms
HW 3.1 – pg 154, 10-13 and 19-30