factoring – general method
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Factoring – General Method. You have learned a variety of methods for factoring. This section puts all of the methods together for a general factoring strategy. - PowerPoint PPT PresentationTRANSCRIPT
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Factoring – General Method
• You have learned a variety of methods for factoring. This section puts all of the methods together for a general factoring strategy.
• It is very important that you can factor a polynomial without being told what method to use. In fact, sometimes several methods will be used on the same problem.
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• A simple version of the factoring strategy is given below.
1. Always factor the Greatest Common Factor first.
2. Determine how many terms are left in the resulting polynomial.
3. Factor using the methods for that number of terms.
4. After completing a step, always ask, can I factor again?
• This is best described in the following diagram.
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Greatest Common Factor
The Greatest Common Factor is always the first step in factoring.
If you leave this step out, the factoring can get extremely difficult or impossible. Don’t forget the GCF!
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Greatest Common Factor
How many terms are there?
Two Three Four
The number of terms determines the possible methods to consider.
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Greatest Common Factor
Lets start with two terms.
Two Three Four
The possible factoring methods include …
Difference of Two Squares
Sum of Two Cubes
Difference of Two Cubes
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Greatest Common Factor
If there are three terms.
Two Three Four
Difference of Two Squares
Sum of Two Cubes
Difference of Two Cubes
Perfect Square Trinomial
Trinomial: Guess/Check
or ac Method
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Greatest Common Factor
If there are four terms.
Two Three Four
Difference of Two Squares
Sum of Two Cubes
Difference of Two Cubes
Perfect Square Trinomial
Trinomial: Guess/Check
or ac Method
Grouping
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• Example 1
Factor:
Factor the GCF
35 20x x
25 4x x
Two terms are left in the resulting polynomial
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Greatest Common Factor
Two Three Four
Difference of Two Squares
Sum of Two Cubes
Difference of Two Cubes
Perfect Square Trinomial
Trinomial: Guess/Check
or ac Method
Grouping
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Greatest Common Factor
Two
Difference of Two Squares
Sum of Two Cubes
Difference of Two Cubes
Consider these three methods
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• Example 1
Factor:
Factor the GCF
35 20x x
25 4x x
Two terms are left in the resulting polynomial
It’s a difference of two squares.
5 2 2x x x
Any more factoring possible? No
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• Example 2
Factor:
Factor the GCF
23 24 48x x
23 8 16x x
Three terms are left in the resulting polynomial
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Greatest Common Factor
Two Three Four
Difference of Two Squares
Sum of Two Cubes
Difference of Two Cubes
Perfect Square Trinomial
Trinomial: Guess/Check
or ac Method
Grouping
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Greatest Common Factor
Three
Perfect Square Trinomial
Trinomial: Guess/Check
or ac Method
Check for a Perfect Square Trinomial first
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• Example 2
Factor:
Factor the GCF
23 24 48x x
23 8 16x x
Three terms are left in the resulting polynomial
It is a perfect square trinomial.
2 2 4 8ab x x
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23 8 16x x
3 4x
3 4x
23 4x
Any more factoring possible? No
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• Example 3
Factor:
Factor the GCF
3 22 9 18x x x
Four terms suggests the grouping method.
None, other than 1
3 22 9 18x x x
2 2 9 2x x x
22 9x x
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22 9x x
Any more factoring possible?
Yes, a difference of two squares.
2 3 3x x x
Any more factoring possible? No
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• With factoring it is important to remember,
after completing a factoring step, always ask
Is there any more factoring possible?
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