Module 0Part 3: Polynomials and Factoring

Obj: To manipulate polynomials and to revisit factoring

Evi: Students will able to solve problems about polynomials

Definition of a Polynomial in x

• Let a0, a1, a2, … , an be real numbers and let n be a nonnegative integer. A polynomial in x is an expression of the form

• + … +• Where . The polynomial is of degree n, an is

the leading coefficient, and a0 is constant term.

Standard Form

• Standard form is when a polynomial is written with descending powers of x.

• EX: • Standard Form:

Adding and Subtracting with Polys

• Step 1: Simplify / Distribute• Step 2: Group like terms• Step 3: Combine like terms• EX:

FOIL that Product

• To find the product of polynomials you must distribute/FOIL

• EX:

• Note: FOIL only works on binomials

Special Products if they matter…

Removing Common Factors

• EX:

Factoring Special Polynomial Forms

Some Examples of Special Factoring

• EX:

“Normal” Factoring

• Yes there is the diamond/box method but that’s like still wearing diapers as a teenager

Factors of a

Factors of cStep 1: Any common factors?Step 2: Think of all possible factorizationsStep 3: Think what adds to middle termStep 4: Solve

Normal Factoring Example

• 6,1 1, 5• 3,2

Factoring by Grouping

• Step 1: Put Parenthesis around the first two and last two

• Step 2:Pull out common factors your parenthesis should match!

• Step 3: Solve