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Common Factoring… the First STEP
Factoring
 is a way of condensing expressions.
 Is the OPPOSITE of FOILING.
 is like a vitamin for your brain.
WHAT are the FACTORS of 27?
A FACTOR is a number that is multiplied with another number, to give you
the answer (in this case, 27).
TRY:
What are Factors of 45?
What is the Greatest Common Factor (GCF) between 27
and 45?_______
We will use this skill in order to FACTOR entire
expressions.
Common Factoring is the FIRST STEP when we are
asked to factor expressions.
How to do it…
1. Find the BIGGEST term that can be divided OUT of
each term (this is called the “GCF” or greatest
common factor).
2. Put that number OUTSIDE a set of BRACKETS.
3. Put what’s left from your divisions, INSIDE
BRACKETS.
Example 1.
Use Common Factoring method to factor:
12 x 2  15 x  6
GCF =
Sometimes the “GCF” is a term that includes letters.
Example 2.
Use Common Factoring method to factor:
12 x 3  15 x 2  6 x
GCF =
Common Factoring: involves finding the largest common factor
between ALL of the terms in an expression. Common factors can have
numbers and/or letters.
Example 3. Factor with Common Factoring method only.
a.
3x 2  6
c.
2 x 2  24 x  70 x3
e.
45a 3  9a 2  18a
b.
d.
5 x  10 y  15
3x 2  6 x  10 x 4
f.
65 x 6  15 x 3  50 x 2
Factoring is the opposite of ___________________________________.
While we will learn several techniques for factoring, we
will ALWAYS try Common Factoring FIRST.
Practice Questions.
1. Factor fully using Common Factor Method.
a. 7 x  35
b. 16  12x
c. 8 x  6 y  2 z
d. 10 x  15 y  20
e. 81x 2  64
f.
25 x 2  49
2. Factor the following expressions using GCF method only.
a. 8 x 2  50
b. 27 x 2  3
c. 36 x 2  100
d. 7 x 2  567
e. 4 x 2  16
f.
x 3  81x
3. What is a GCF? _______________________________________________________
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