Algebra I Class Notes
Topic: Intro to Polynomials
Warm-up:
You are gathering an order from your friends to place for lunch. How would you group/categorize the following
using variables to simplify the order:
● 2 hamburgers, 3 cheeseburgers, 1 more hamburger, 4 more cheeseburgers, 2
double cheeseburgers
Now add the following to the order:
● 4 hamburgers, 6 napkins, 2 hamburgers 5 double cheeseburgers, remove 3
hamburgers, add 8 double cheeseburgers, and finally add 2 hamburgers
A few more friends are hungry, now add the following:
● 1 cheeseburger, 3 double cheeseburgers, 11 napkins, 5 cheeseburgers, 9
hamburgers, take off 1 double cheeseburger, 9 napkins
Final order:
Topic: Adding and Subtracting Polynomials
Steps for adding and subtracting
1. Identify Like Terms
2. Rearrange terms so that like terms are together.
3. Combine Like terms
Add or Subtract
A monomial is a number, a variable, or a product of numbers and variables with whole-number exponents.
Monomial examples: 5
x
-7xy 0.5x4
A degree of a monomial is the sum of the exponents of the variables. A constant has degree 0.
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.
The standard form of a polynomial that contains one variable is written with the terms in order from greatest degree to least
degree.
Find the degree of each monomial:
-2a2b4
4
8y
0.5x2y + 0.25xy + 0.75
6x4 + 9x2 – x + 3
Find the degree of each polynomial:
4x – 18x5
Write each polynomial in standard form. Then give the leading coefficient.
20x – 4x3 + 2 – x2
y3 + y5 + 4y
Some polynomials have special names based on their degree and the number of terms they have:
Degree
Name
0
Constant
1
Linear
2
Quadratic
3
Cubic
4
Quartic
5
Quintic
6 or more
6th degree, 7th degree and so on
Terms
1
2
3
4 or more
Classify each polynomial according to its degree and number of terms:
5x – 6
y2 + y + 4
6x7 + 9x2 – x + 3
Name
Monomial
Binomial
Trinomial
Polynomial