1. Today's Goals:
 Introduction to Factoring the GCF
03/12/15
 Review for Test: Polynomial Operations
 Document: Test Review/Notes
Continuing Concepts:
New Concepts:
 Expanding Binomials/Factoring Trinomials

2. Find the area of the triangle:
x2
+ 1
2x - 4
x3
- 2x2
+ x - 2
Test Review:
bh
2
10y2
+ 7y + 64ft.

3. Test Review:
(2a2
b + b2
)2
Expanding Binomials:
Factoring Trinomials:
(8x3
- 18x) Common Factors? 2x(4x2
- 9)
Factor Complete? 2x(2x+3)(2x - 3)
Which brings us to today's topic: Factoring the GCF

5. Factoring the GCF:
We'll start by distributing the monomial
Starting with the coefficients, and then the variables,
is there anything all three terms have in common? If
so, factor it out, then determine what is left.
The point of factoring is to simplify
1) 3x(2x2 – 3x + 4)
Factor:
2) 14x3y + 7x2y –
7xy
= 6x3 – 9x2 + 12x
= 7xy(2x2 + x – 1)

6. Factors: Quantities that are multiplied together to form a product.
3 • 4 = 12
Factors Product
An algebra example:
(x + 2)(x + 3) =
Factors Product
x2
+ 5x + 6
There are several methods that can be used when factoring
polynomials. The method used depends on the type of
polynomial that you are factoring.
We will spend the next few weeks learning to factor by:
1. Greatest Common Factor 2. Grouping 3. Difference of Squares
4. Sum or Difference of Cubes 5. Special Case Trinomials
Factoring Polynomials

7. ** Remember that the method of factoring depends on the type
of polynomial being factored. Throughout this process, pay
attention not only on how to factor, but the type of polynomial
being factored. As we progress, you will have to correctly match
the factoring method with the polynomial.
Factoring Polynomials
Greatest Common Factor: GCF
Pros: -- simple to understand
Cons: -- most polynomials cannot be completly factored this way
Factoring Method #1
Whole numbers that are multiplied together to find a
product are called factors of that product. A number is
divisible by its factors. 2•2 •3 =12

8. When factoring polynomials, the first step is to ALWAYS look for a
GCF. If so, it is factored out. The remaining polynomial may or may
not be able to be simplified further using other methods.
Prime factorization is used to make sure you have the GCF.
Factoring Polynomials
Example 1: Writing Prime Factorizations
Write the prime factorization of 98.
Factor tree Method
Choose any two factors of 98 to
begin. Keep finding factors until
each branch ends in a prime factor.
98 = 2 7 7
The prime factorization of 98 is 2  7  7 or 2  7298
2 49
7 7

 

9. Simplify by finding the GCF
(26x3y2 z3)(52xy4z2) = The GCF of 26 and 52 is
26xy2z2
Factoring the GCF: (2)
213  xxxyyzzz
2213 xyyyyzz
The simplified product is 26xy2z2(2x2y2z)

10. Handout:
 The one document you can use with your test
Each version of the test will have a problem from the
handout on it.
You can submit your completed document with your test
for extra credit.