Name
LESSON
8-6
Date
Class
Reteach
Choosing a Factoring Method
Use the following table to help you choose a factoring method.
First factor out a GCF if possible. Then,
check for
difference of
squares.
If binomial,
check for
perfect square
trinomial.
If trinomial,
yes
no
Use a ⫹ b a ⫺ b .
If no GCF, it cannot be factored.
yes
no
2
2
Factor using a ⫹ b or a ⫺ b .
If a ⫽ 1, check factors of c that sum to b.
If a ⫽ 1, check inner plus outer factors of
a and c that sum to b.
If 4 or more
terms,
Try to factor by grouping.
Explain how to choose a factoring method for x 2 ⫺ x ⫺ 30. Then state the method.
•
There is no GCF.
•
x 2 ⫺ x ⫺ 30 is a trinomial.
•
The terms a and b are not perfect squares, therefore this is not a perfect square
trinomial.
•
a⫽1
Method: Factor by checking factors of c that sum to b.
Explain how to choose a factoring method for 2x 2 ⫺ 50. Then state the method.
•
Factor out the GCF: 2 x 2 ⫺ 25 •
x 2 ⫺ 25 is a binomial.
•
a and b are perfect squares. This is a difference of squares.
Method: Factor out GCF. Then use a ⫹ b a ⫺ b .
Explain how to choose a factoring method for each polynomial. Then
state the method.
2
no GCF; x ⫹ 14x ⫹ 49 is a trinomial;
2
1. x ⫹ 14x ⫹ 49
2. 4x 2 ⫺ 40
3.
This is a perfect square trinomial. Method: use a ⫹ b 2.
2
2
factor out the GCF: 4 x ⫺ 10 ; x ⫺ 10 is a binomial;
This is not a difference of squares. Method: Factor out GCF.
2
2
factor out the GCF: 2 x ⫹ 4x ⫹ 3 ; x ⫹ 4x ⫹ 3 is a
2x 2 ⫹ 8x ⫹ 6
trinomial; This is not a perfect square trinomial; a ⫽ 1;
Method: Factor out GCF. Then find factors of c that sum to b.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c08-6_rt.indd 46
46
Holt Algebra 1
12/26/05 8:13:23 AM
Process Black
Name
Date
Class
Reteach
LESSON
8-6
Choosing a Factoring Method (continued)
It is often necessary to use more than one factoring method to factor a polynomial completely.
2
Factor 5x ⫺ 5x ⫺ 60 completely.
Check your answer.
2
Factor 16x ⫺ 36 completely.
Check your answer.
Step 1: Factor out the GCF.
Step 1: Factor out the GCF.
5x 2 ⫺ 5x ⫺ 60
16x 2 ⫺ 36
5 x 2 ⫺ x ⫺ 12 4 4x 2 ⫺ 9 Step 2: Choose a method for factoring.
Step 2: Choose a method for factoring.
•
x ⫺ x ⫺ 12 is a trinomial.
•
4x 2 ⫺ 9 is a binomial.
•
It is not a perfect square.
•
It is a difference of squares.
2
Method: Find factors of c that will sum to b.
Method: Use a ⫹ b a ⫺ b .
Step 3: Factor.
Step 3: Factor.
Factors of ⫺12
Sum
2 and ⫺6
3 and ⫺4
⫺4 7
⫺1 3
4x 2 ⫺ 9
a ⫽ 2x, b ⫽ 3
2x ⫹ 3 2x ⫺ 3 x ⫹ 3 x ⫺ 4 Step 4: Write the complete factorization.
Step 4: Write the complete factorization.
4 2x ⫹ 3 2x ⫺ 3 5 x ⫹ 3 x ⫺ 4 Check:
Check:
4 2x ⫹ 3 2x ⫺ 3 ⫽ 4 4x 2 ⫺ 6x ⫹ 6x ⫺ 9 5 x ⫹ 3 x ⫺ 4 ⫽ 5 x 2 ⫺ 4x ⫹ 3x ⫺ 12 ⫽ 4 4x 2 ⫺ 9 ⫽ 5 x 2 ⫺ x ⫺ 12 ⫽ 16x 2 ⫺ 36 3
⫽ 5x 2 ⫺ 5x ⫺ 60 3
Factor each polynomial completely.
2
4. 3x ⫺ 300
3 x ⫹ 10 x ⫺ 10 7. ⫺7x 2 ⫺ 21x ⫹ 28
⫺7 x ⫹ 4 x ⫺ 1 Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c08-6_rt.indd 47
5. 4x 2 ⫺ 20x ⫺ 24
4 x ⫹ 1 x ⫺ 6 8. 8x 2 ⫺ 18
6. 8x 2 ⫺ 40x ⫹ 50
2 2x ⫺ 5 2
9. 20x 2 ⫹ 50x ⫹ 30
2 2x ⫹ 3 2x ⫺ 3 47
10 2x ⫹ 3 x ⫹ 1 Holt Algebra 1
12/26/05 8:13:24 AM
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