Chapter 7 Factoring. Chapter 7 Factoring A General Approach to Factoring 7.4 A General Approach to Factoring.

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Presentation transcript:

Chapter 7 Factoring

A General Approach to Factoring 7.4 A General Approach to Factoring

7.4 A General Approach to Factoring Objectives Factor out any common factor. Factor binomials. Factor trinomials. Factor polynomials with more than three terms. Copyright © 2010 Pearson Education, Inc. All rights reserved.

7.4 A General Approach to Factoring Factoring a Polynomial A polynomial is completely factored when it is written as a product of prime polynomials with integer coefficients, and none of the of polynomial factors can be factored further. Copyright © 2010 Pearson Education, Inc. All rights reserved.

7.4 A General Approach to Factoring Factoring Out a Common Factor This step is always the same, regardless of the number of terms in the polynomial. Factor each polynomial. (a) (b) (c) Copyright © 2010 Pearson Education, Inc. All rights reserved.

7.4 A General Approach to Factoring Factoring Binomials Copyright © 2010 Pearson Education, Inc. All rights reserved.

7.4 A General Approach to Factoring Factoring Binomials Use one of the rules to factor each binomial if possible. (a) (b) Copyright © 2010 Pearson Education, Inc. All rights reserved.

7.4 A General Approach to Factoring Factoring Binomials Use one of the rules to factor each binomial if possible. (c) (d) Sum of cubes is prime. It is the sum of squares. The binomial 25m2 + 625 is the sum of squares. It can be factored, however as 25(m2 + 25) because it has a common factor, 25. Copyright © 2010 Pearson Education, Inc. All rights reserved.

7.4 A General Approach to Factoring Factoring Trinomials Copyright © 2010 Pearson Education, Inc. All rights reserved.

7.4 A General Approach to Factoring Factoring Trinomials Factor each trinomial. (a) (b) (c) The numbers -6 and 1 have a product of -6 and a sum of -5. Copyright © 2010 Pearson Education, Inc. All rights reserved.

7.4 A General Approach to Factoring Factoring Trinomials Factor each trinomial. (d) (e) Copyright © 2010 Pearson Education, Inc. All rights reserved.

7.4 A General Approach to Factoring Factoring Polynomials with More than Three Terms Factor each polynomial. Consider factoring by grouping. (a) (b) Group the terms. Factor each group. 5k + 1 is a common factor. Difference of squares Group the first three terms. Perfect square trinomial Difference of squares Copyright © 2010 Pearson Education, Inc. All rights reserved.

7.4 A General Approach to Factoring Factoring Polynomials with More than Three Terms Factor each polynomial. Consider factoring by grouping. (a) Rearrange and group the terms. Factor each group. Factor out 2m – n. Copyright © 2010 Pearson Education, Inc. All rights reserved.