1. Polynomials −𝟑𝒙 𝟔 + 𝟒𝒙 𝟒 −𝟖𝒙 𝟑 + 𝟏𝟔 My Definition:
TextbookDefinition: An expression which is the sum of terms of the form axk where k is a nonnegative integer.
EXAMPLE:
−𝟑𝒙 𝟔 + 𝟒𝒙 𝟒 −𝟖𝒙 𝟑 + 𝟏𝟔
My Definition:

2. Important Parts of a Polynomial
Leading Coefficient: ______________________________________
__________________________________________
Degree of a Polynomial: __________________________________
Constant: _______________________________________________

3. Polynomials
Chapter 10.1

4. Polynomials
TextbookDefinition: An expression which is the sum of terms of the form axk where k is a nonnegative integer.
a is a coefficient
x is a variable
k is an exponent
EXAMPLE: 5y2
EXAMPLE:
−𝟑𝒙 𝟔 + 𝟒𝒙 𝟒 −𝟖𝒙 𝟑 + 𝟏𝟔
My Definition: A string of terms connected with + and – signs. All exponents must be positive & can’t be fractions.

5. Not Polynomials

6. Polynomials in STANDARD FORM largest exponent to smallest exponent
A polynomial is in standard form when the terms are written from
largest exponent to smallest exponent

7. Important Parts of a Polynomial
Leading Coefficient: When the polynomial is written in standard form, this is the coefficient of the first term
Degree of a Polynomial: The largest exponent of all the terms
Constant: A term with no variable

8. Rewrite in Standard Form
Rewrite in Standard Form. Identify the leading coefficient, the degree of the polynomial and constants.

9. Classifying Polynomials by degree & number of terms9

10. Classifying Polynomials by degree & number of terms
More than 3 terms doesn’t get a special name 10

11. Adding & Subtracting Polynomials
Chapter 10.1

12. Adding Polynomials
Write the first expression in standard form. Leave Space or Write Zero for any “missing exponents”.
Write next expression beneath, aligning like terms (same variable, same exponent)
Add coefficients and constants.
***Exponents stay as they are! 12

13. Subtracting Polynomials
Write the first expression in standard form. Leave Space or Write Zero for any “missing exponents”.
Write next expression beneath, aligning like terms (same variable, same exponent)
Subtract the coefficients and constants. ***Exponents stay as they are!
NOTE: IT HELPS TO DISTRIBUTE THE NEGATIVE
In other words, change all signs of bottom polynomial 13

14. Multiplying Polynomials
It’s just the distributive property!
When you multiply polynomials, remember that EACH Term of one polynomial must be multiplied by EACH Term of the other.
When multiplying variables, use the property
xa ∙ xb = xa + b