1. Operations and equations
Polynomials
Operations and equations

2. Subtracting Polynomials
Setting up foldable
Adding Polynomials +
Subtracting Polynomials -
Multiplying Polynomials ×
Dividing Polynomials ÷
Is called factoring, see page R33

3. Adding and Subtracting Polynomials
Line up like terms (collect like terms) Like terms: terms that have the same variable and exponent
Add coefficients coefficient: number in front of variable
𝟒 𝒙 𝟐 +𝟑 𝒙 𝟑 +𝒙 +( 𝒙 𝟑 −𝟐 𝒙 𝟐 +𝟑𝒙)
𝟒 𝒙 𝟐 +𝟑 𝒙 𝟑 +𝒙 −( 𝒙 𝟑 −𝟐 𝒙 𝟐 +𝟑𝒙)
Line up like terms (collect like terms)
Subtract coefficients

4. Multiplying Polynomials
Terms: constants, variable, product of variables and constants (monomial),separated by addition or subtraction.
Box Method:
The number of rows match with the number of terms in the first factor. The number of columns match with number of terms in the second factor.
(𝟑𝒙+𝟐)(𝟒𝒙+𝟕) F O I L
FOIL:
F first terms in parentheses
O terms toward outer parentheses
I terms toward inner parentheses
L last terms in parentheses

5. Defining Polynomials Polynomial Illustration
Polynomials are named by their degree and number of terms.
𝟓𝒙 𝒚 𝟐 −𝟑𝒙+𝟓 𝒚 𝟑 −𝟑
Cubic polynomial
Definition
An expression that can have constants, variables, and exponents, but:
No division by a variable
Only whole number exponents
It can’t have an infinite number of terms
Non-example
2 𝑥 𝑥+ 𝑦 −2 5 𝑥 1 2
Polynomial

6. Naming Polynomials

7. Greatest Common Factor Difference of Two squares
Setting up foldable
Greatest Common Factor
GCF
Difference of Two squares
Quadratic Trinomial
A=1
A>1

8. GCF and difference of squares
Looking for the highest number and/or the lowest exponent on the variable that divides evenly into all terms
Standard Form:
Listing the terms of the polynomial from greatest to least
Qualifying Questions
( 𝒂 𝟐 − 𝒃 𝟐 )
Is it a binomial?
Are we subtracting?
Are both terms perfect squares?
If yes to ALL 3 ?’s
Then,
Take the square root of both terms and plug into
(𝒂−𝒃)(𝒂+𝒃)

9. Factoring Quadratic Trinomials
Quadratic is in standard form
The coefficient of the middle term is the SUM
The last term is the PRODUCT
Draw your x and find the two numbers that satisfy the conditions
Write answer as a product two binomials
Slide the coefficient of the leading term to the last and multiply the two #s
Divide and bottoms up