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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.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 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 Factoring Factored form Product

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 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. Product of x and x is x 2. Product of 5 and –7 is –35. Sum of the product of outer and inner terms OI F L

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 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 - 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 - 12 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. Sec 7.2 - 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 –10.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 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 - 15 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 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 - 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, 3x 2 and –2, respectively.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Sec 7.2 - 18 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. Sec 7.2 - 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 - 21 7.2 Factor Trinomials Factoring a Polynomial Using Substitution Remember to make the final substitution of (x – 2) for y. CAUTION