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Factoring Notes Math 117
I have been asked to explain how and when you know to factor.
I will be taking problems from the text in chapter 5.
When I teach this in a lecture format, I provide my students with a checklist to follow.
When factoring, look for the following:
1)
Always look to see if there is a common factor to take out. If there, is, take it out and continue factoring what is left if
possible.
Example 1a Factor x
9
y
6
– x
7
y
5
– x
4
y
4
– x
3
y
3
Looking at this problem, I see that I have an x
3
and a y
3
common. When dealing with exponents, I always take the smallest one if each
terms has that variable.
X
3
y
3
(x
6
y
3
– x
4
y
2
– xy – 1)
At this point, we could try to factor what is left in the parentheses, but it will not factor.
Example 1b
2x
2
– 2x – 8
We have a 2 in common with each term so we factor that out.
2(x
2
– x – 4)
Again, we look to see if the middle is factorable, but it is not. So this is our answer.
2)
If the problem has two terms, look for a difference of squares.
Example 2a:
16x
2
– 25y
2
This is a difference of squares because it is subtraction and the terms are perfect squares. I.e. 16x
2
= (4x)
2
and 25y
2
= (5y)
2
So this factors to
(4x + 5y)(4x – 5y)
Example 2b:
24x
2
– 54
At first glance, this may not look like a difference of squares, but remember step 1. We need to factor our the common factor here
which is 6. So we have
6(4x
2
– 9)
Now the 4x
2
– 9 is factorable to
2x – 3 and 2x + 3
So our answer is
6(2x+3)(2x3)
3)
If we have three terms of the form
x
2
+ bx + c, we have a leading coefficient of 1.
Remember the leading coefficient is the number with the first term (1x
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 Spring '09
 RANJITREBELLO

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