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Name __________________________________
Date _____________________ Period ________
Algebra II Honors
5-4 Factoring
Notes Sheet
______________________ a polynomial means expressing it as a _____________________ of other
polynomials.
Factoring Method #1: Factoring polynomials with a common ________________________ factor
(________________).
**__________________________________________________________________________
Steps:
1. ____________________________________________________________________
2. ____________________________________________________________________
3. ____________________________________________________________________
Do you remember how to find the GCF of numbers?
The first method is to list all of the factors of each number, then list the common
factors and choose the largest one.
The second method for finding the greatest common factor is to list the prime
factors, then multiply the common prime factors.
Example: 6c 3d  12c 2 d 2  3cd
Try these on your own!
1. 6 x3  3x 2  12 x
2. 5 x 2  10 x  35
3. 16 x3 y 4 z  8x 2 y 2 z 3  12 xy3 z 2
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Factoring Method #2: Factoring polynomials that are a __________________________________.
Difference of Perfect Squares: When factoring using a difference of perfect squares, look for the
following three things:
1.
2.
3.
**If all three of the above are true, write two parentheses, one with a plus sign, and one with a
minus sign. The terms in each of the parentheses will be the square root of each term.
A difference of perfect squares is a BINOMIAL (for two terms only!) and it factors like this:
2
2
a  b  (a  b)(a  b)
**Because multiplication is commutative, you can reverse the +/- without changing the problem.
Example: x 2  16
Example:
1 2
x  81
49
Try these on your own:
1. x 2  121
2. 9 y 2  169 x 2
3. x 4  16
Factoring Method #3: Factoring by Grouping




When polynomials contain _______ terms, it is sometimes easier to group terms in order to
factor.
Your goal is to create a ______________________________________.
You can also move terms around in the polynomial to create a common factor.
Practice makes it easier to recognize common factors.
Steps:
1. Group the first two terms and the last two terms by putting parentheses around them.
2. Factor out the GCF from each group so that both sets of parentheses contain the same
factors.
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3. Factor our GCF again and write the answer as the product of two binomials.
Example: b3  3b 2  4b  12
Example: 2 x 3  16 x 2  8 x  64
Factoring Chart: This chart will help you determine which method of factoring to use.
Type
Number of Terms
1.
2.
3.
4.
Factoring Method #4: Trinomials – Trial and Error – Box
Box method:
1. Make a box with four squares
2. Make sure that the terms of the trinomial are in descending order.
3. Put the first term in the top left box.
4. Put the last term in the bottom right box.
5. Multiply those two terms together.
6. List factors of the product in #5 that will add together to get the middle term.
7. Put those in the other two boxes.
8. Find the GCF of each row and column – that is your trinomial factored.
Example: x 2  7 x  6
Example: 2a 2  3a  1
3
Example: 6c 2  13c  6
Example: 12m 2  m  6
More examples:
1. 2 x 2  9 x  10
2. 6 y 2  13 y  5
3. 12 x 2  11x  5
4. 5 x  6  x 2
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