Factoring Trinomials

Contributed by:

Sharp Tutor Mon, Jan 17, 2022 06:52 PM UTC

OBJECTIVE:
1. Factor trinomials when the coefficient of the squared term is 1. 2. Factor trinomials when the coefficient of the squared term is not 1. 3. Use an alternative method of factoring trinomials. 4. Factor by substitution.

1. Copyright © 2010 Pearson Education, Inc. All rights reserved
Sec 7.2 - 1

2. Chapter 7
Factoring
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Sec 7.2 - 2

3. 7.2
Factoring Trinomials
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Sec 7.2 - 3

4. 7.2 Factoring Trinomials
Objectives
1. Factor trinomials when the coefficient of
the squared term is 1.
2. Factor trinomials when the coefficient of
the squared term is not 1.
3. Use an alternative method of factoring
trinomials.
4. Factor by substitution.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 4

5. 7.2 Factor Trinomials
Factor Out the Greatest Common Factor
The product of two binomials sometimes gives a trinomial. For
example:
So, we have two processes that “undo” each other.
Multiplying
Factored form Product
Factoring
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 5

6. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient of the Squared Term is 1
Multiplying binomials uses the FOIL method, and factoring
involves using the FOIL method backwards.
2
Product of x and x is x.
F
L Product of 5 and –7 is –35.
Sum of the product of outer and inner terms
O I
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7. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is 1
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 7

8. 7.2 Factor Trinomials
Factoring Trinomials in Form
Step 1 Step 2
Coefficient
of middle
term
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9. 7.2 Factor Trinomials
Factoring Trinomials in Form
The required numbers are –8 and 4, so
You should always check your answer by multiplying the
factors to see if you get the original polynomial.
Guidelines for Factoring Trinomials
1. If the last term is positive, the factors will have the form
( ___ + ___ ) ( ___ + ___ ) or ( ___ – ___ ) ( ___ – ___ )
The + or – sign is determined by the coefficient of the middle term.
2. If the last term is negative, the factors will have the form
( ___ + ___ ) ( ___ – ___ ) or ( ___ – ___ ) ( ___ + ___ )
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 9

10. 7.2 Factor Trinomials
Factoring a Trinomial With A Common Factor
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11. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 11

12. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 12

13. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Listing all the pairs of
numbers whose product
is –24 to find a pair
whose sum is –10, only
2 and –12 have a sum of
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 13

14. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 14

15. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Factoring Other Trinomials by Trial and Error
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16. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Factoring Other Trinomials by Trial and Error
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 16

17. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Factoring Other Trinomials by Trial and Error
Here are the possibilities, each of which produces the correct
first and last term, 3x2 and –2, respectively.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 17

18. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Trial and Error (Alternative Method) Summarized
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20. 7.2 Factor Trinomials
Factoring a Polynomial Using Substitution
Sometimes we can factor more complicated problems by
substituting a variable for an expression.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 20

21. 7.2 Factor Trinomials
Factoring a Polynomial Using Substitution
CAUTION
Remember to make the final substitution of (x – 2) for y.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 21

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