This document provides information about factoring different types of polynomials: 1) Monomials can be factored if the terms are a multiple of something. Binomials can be factored if both terms are a multiple of the same number. Trinomials can be factored if there is a common multiple of all three terms or if they are the product of two binomials. 2) Examples are provided for factoring monomials, binomials, and trinomials. For trinomials, all terms must be a multiple of the same number or factor or they can be written as the product of two binomials using the F.O.I.L. method.

1. Factoring Review
10I.A.5
Demonstrate an
understanding of common
factors and trinomial factoring,
concretely, pictorially, and
symbolically.

2. Dictionary
Polynomial: a term with many parts ex. x 2 + 3x + 6
Monomial: a term with one part ex. 4x
Binomial: a term with 2 parts ex 3x + 6y
Trinomial: a term with 3 parts ex. x 2 + 3y + 7
Factor: part of the whole

3. Factoring Monomials
Monomials can be factored if the terms is a multiple of
something.
example
factor 8x2
solution
2(2)(2)xx
What are the factors of 9x4?

4. Factoring Binomials
Binomials can be factored if both parts are a multiple
of the SAME number
Example 1
factor 3x + 5x
Solution
both parts are a
multiple of x
x(3+5) = 8x
Example 2
2
factor 2x - 8x
Solution
both terms are a
multiple of 2 and x
2x (x-4)
Example 3
factor 3x2 + 4y
Solution
this cannot be factored
because there is no common
multiple
What are the factors of
( 5x3y2 + 25xy )

5. Factoring Trinomials
Trinomials can be factored if there is a common
multiple of ALL 3 terms
Example 1
factor 2x3 + 4x2 + 16x
Solution
all terms are a multiple of 2 and x
2x (x2 +2x +8)
Trinomials can also be a product of 2 binomials
REMEMBER: F.O.I.L
(x + 2) (x + 3) = x2 + 5x + 6
so the factors of x2 + 5x + 6 are
(x + 2) (x + 3)

6. What are the factors of
x 2 + 6x + 5
What steps did you follow to find the factors?