1. Introduction to Polynomials
CCM2 11-1

2. Monomials and degree
Monomials (or terms) are the product of real numbers and variables. Each variable has an exponent called a power.
The number at the front of the variables is called the coefficient. When no coefficient is shown it is “1.”
The degree of a monomial is the sum of the exponents of the variables. Remember when no exponent is shown, it is “1.”
Examples: x xy x3y
Example: x xy 2x3y
Coefficient: n/a
Degree:

3. Monomial and Term Names
Monomials are named by their degree
Degree
Name
Example
Constant 5 1
Linear Term 3x 2
Quadratic Term
4x2 3
Cubic Term
2x3 4
Quartic Term
6x4
5th-Degree Term
3x5

4. polynomials and degree
Polynomials are the sum or difference of monomials.
The degree of a polynomial is the same as its highest degree term. This term determines the polynomials overall shape.
Examples: x2 - 6x or x3y - 4
Example: x2 + 6x x3y + 4
Degree:

5. Classifying Polynomial
Classify Polynomials by degree and number of terms.
The degree name is that of its highest degree term.
The number of terms are described as follows
Number of Terms
Name
Example 1
Monomial 5x 2
Binomial
3x2 + 7 3
Trinomial
4x2 + 2x + 1

6. You Try Classify the following Polynomials Example Name 5x
Linear Monomial
3x2 -2x + 7
Quadratic Trinomial
2x + 1
Linear Binomial
5x4 - 2
Quartic Binomial
3x3 -5x + 7
Cubic Trinomial

7. Standard Form
Arrange the terms starting with the highest degree term and ending with the lowest degree term.
For example: x2 + 7 – 4x becomes x2 – 4x +7
The coefficient of the highest degree term is called the “Leading Coefficient” because it is the first coefficient of the polynomial in standard form. It determines how wide or narrow the polynomial is, with numbers closer to 0 being wider.

8. ADDING or subtracting Polynomials (Horizontal Method)
If subtracting, distribute the negative first
Combine like terms
(like terms have the same variables and powers.)
Example: (x2 + 6x + 8) - (3x - 2)
x2 + 6x x + 2
x2 + 3x + 10

9. ADDING or subtracting Polynomials (Vertical Method)
Write one polynomial over the other like you would for numbers. Make sure to align like terms in the same columns
Add or subtract each column as indicated
x2 + 6x + 8
x - 2
x2 + 9x + 6
x2 + 6x + 8
x - 2
x2 + 3x +10

10. Summary Identified the key parts of a polynomial
Classified polynomials
Add and subtract polynomials
Horizontal Method
Vertical Method
Thank You