Chapter 7 Factoring

7.2 Factoring Trinomials

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

Factor Out the Greatest Common Factor 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.

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. Product of x and x is x2. F L Product of 5 and –7 is –35. Sum of the product of outer and inner terms O I Copyright © 2010 Pearson Education, Inc. All rights reserved.

7.2 Factor Trinomials Factoring Trinomials When the Coefficient of the Squared Term is 1 Copyright © 2010 Pearson Education, Inc. All rights reserved.

Factoring Trinomials in Form 7.2 Factor Trinomials Factoring Trinomials in Form Step 1 Step 2 Coefficient of middle term Copyright © 2010 Pearson Education, Inc. All rights reserved.

Factoring Trinomials in Form 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 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. If the last term is negative, the factors will have the form ( ___ + ___ ) ( ___ – ___ ) or ( ___ – ___ ) ( ___ + ___ ) Copyright © 2010 Pearson Education, Inc. All rights reserved.

Factoring a Trinomial With A Common Factor 7.2 Factor Trinomials Factoring a Trinomial With A Common Factor Copyright © 2010 Pearson Education, Inc. All rights reserved.

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

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

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 –10. Copyright © 2010 Pearson Education, Inc. All rights reserved.

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

Factoring Other Trinomials by Trial and Error 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.

Factoring Other Trinomials by Trial and Error 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.

Factoring Other Trinomials by Trial and Error 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.

Trial and Error (Alternative Method) Summarized 7.2 Factor Trinomials Factoring Trinomials When the Coefficient of the Squared Term is Not 1 Trial and Error (Alternative Method) Summarized Copyright © 2010 Pearson Education, Inc. All rights reserved.

7.2 Factor Trinomials Copyright © 2010 Pearson Education, Inc. All rights reserved.

Factoring a Polynomial Using Substitution 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.

Factoring a Polynomial Using Substitution 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.

7.2 Factor Trinomials Copyright © 2010 Pearson Education, Inc. All rights reserved.