copyright © 2010 pearson education, inc. all rights reserved sec 7.2 - 1


Factoring

Chapter 7


7.2

Factoring Trinomials

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


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

Factoring

Factored form Product



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.

Product of x and x is x2.

Product of 5 and –7 is –35.

Sum of the product of outer and inner terms

O I

F

L



Factoring Trinomials When the Coefficient

of the Squared Term is 1



Factoring Trinomials in Form

Step 1 Step 2

Coefficient of middle term



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 ( ___ – ___ ) ( ___ + ___ )



Factoring a Trinomial With A Common Factor


7.2 Factor TrinomialsFactoring Trinomials When the Coefficient

of the Squared Term is Not 1




Solution




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 –10.




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.




Trial and Error (Alternative Method) Summarized



Factoring a Polynomial Using Substitution

Sometimes we can factor more complicated problems by substituting a variable for an expression.



Factoring a Polynomial Using Substitution

Remember to make the final substitution of (x – 2) for y.

CAUTION

copyright © 2010 pearson education, inc. all rights reserved sec 7.2 - 1

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