Bellwork 5-1
Please check your answers with the key on the board. Then, be ready to ask questions if you have them.
Lesson 5-2: Polynomials
After this lesson, TSWBAT perform operations on polynomials including
 identify a polynomial
 add, subtract and multiply a polynomial
A monomial is either a real number, a variable or a
product of real numbers and variables with whole
number exponents. Examples of monomials are:



-8
4xy
-2x2
A polynomial is the sum or difference of
monomials. Examples of polynomials are:


3x2
-15x5 -- 6x3 + 3x + 4
A polynomial is written in standard form if the
exponents for each monomial are in descending order
(greatest to least).
We can classify polynomials be degree or by the
number of terms.
Your Turn!
Take a minute to fill out the “Name” column in the table below. Use the words MONOMIAL,
TRINOMIAL, POLYNOMIAL OF 4 TERMS, and BINOMIAL. Each word will be use ONCE.
Number
of Terms
Example
1
4x
2
5x - 3
3
4x4 + 3x3 - 5x2
4 or more
2x3 - 5x2 + 3x - 1
Name
The degree of a polynomial is the HIGHEST exponent in the polynomial.
Your Turn!
Take a minute to fill out the “Degree” column in the table below. Make sure to READ the
definition above.
Degree
Example
5
4x + 2
Name
Constant
Linear
2x2 - 3
Quadratic
5x3 + 2x2 - 1
Cubic
-2x4 + 3x3
Quartic
x5 - 3x3 + 2x - 5
Quintic
Anything over a degree of 5 is stated as the nth degree polynomial.
Your Turn, Again!
Classify each of the following polynomials by the number of terms.
1. 5x3 + 2x + 1
2. -5x
3. 2x4 + 3x3
Classify each of the following polynomials by its degree.
1. 5x2 + 2x + 1
2. -5x
3. 2x4 + 3x3
4. -6
Adding and Subtracting Polynomials
We can add or subtract polynomials simply by combining like terms, terms with exactly the
same variable including the exponent. For example:
 5x2 - 3x2, CAN be combined by adding the coefficients and keeping the same variable and
exponent. Therefore:
5x2 - 3x2 = 2x2
 7x3 + 5x2, CANNOT be added because the exponents on the variables are different.
Ex. 1:
Ex. 2:
Practice
Multiplying Polynomials
We can also multiply polynomials, using the distributive property and the laws of exponents.
Recall that the multiplication property for exponents says that to multiply powers with
the same base we add the exponents. For example:
 5x2(-2x5) = -10x2 + 5 = -10x7
There are two methods that we are going to look at for multiplying polynomials: using the
distributive property (aka FOIL in some cases) and using a box.
Ex. 1:
Ex. 2:
Practice
5-2 More Practice