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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Section 5.3 Factoring Polynomials.

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1 Copyright © 2013, 2009, 2005 Pearson Education, Inc. Section 5.3 Factoring Polynomials

2 Copyright © 2013, 2009, 2005 Pearson Education, Inc. Objectives Common Factors Factoring and Equations Factoring by Grouping

3 Copyright © 2013, 2009, 2005 Pearson Education, Inc. Common Factors When factoring a polynomial, we first look for factors that are common to each term. By applying the distributive property, we can write a polynomial as two factors. For example: It can be factored as follows:

4 Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Factor. a.b.c.d. Solution a.b.

5 Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example (cont) Factor. a.b.c.d. Solution c.d.

6 Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Factor. a.b. Solution a. b.

7 Copyright © 2013, 2009, 2005 Pearson Education, Inc. Factoring and Equations To solve equations using factoring, we use the zero- product property. It states that, if the product of two numbers is 0, then at least one of the numbers must equal 0.

8 Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Solve each equation. a.b. Solution a.b.

9 Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Solve each polynomial equation. a.b. Solution a. We begin by factoring out the greatest common factor. b. We begin by factoring out the greatest common factor. No real number can satisfy x 2 = –1, the only solution is 0.

10 Copyright © 2013, 2009, 2005 Pearson Education, Inc. Polynomial equations can also be solved numerically and graphically.

11 Copyright © 2013, 2009, 2005 Pearson Education, Inc.

12 Example Solve the equation 6x – x 2 = 0 numerically, graphically, and symbolically. Solution Numerical: Make a table of values. xy Graphical: Plot the points in the table. The intercepts are the solution to the equation.

13 Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example (cont) Solve the equation 6x – x 2 = 0 numerically, graphically, and symbolically. Solution Symbolic: Start by factoring the left side of the equation. Note that the numerical and graphical solutions agree with the symbolic solutions.

14 Copyright © 2013, 2009, 2005 Pearson Education, Inc.

15 Example Factor. a. 3x(x + 1) + 4(x + 1)b. 3x 2 (2x – 1) – x(2x – 1) Solution a. Both terms in the expression contain the binomial x + 1. Use the distributive property to factor. b.

16 Copyright © 2013, 2009, 2005 Pearson Education, Inc.

17 Example Factor the polynomial. Solution

18 Copyright © 2013, 2009, 2005 Pearson Education, Inc. Example Factor the polynomial. Solution


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