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**Factoring Polynomials**

Section 5.3 Factoring Polynomials

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**Objectives Common Factors Factoring and Equations**

Factoring by Grouping

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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:

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Example Factor. a. b. c. d. Solution a. b.

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Example (cont) Factor. a. b. c. d. Solution c. d.

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Example Factor. a. b. Solution a. b.

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**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.

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Example Solve each equation. a. b. Solution

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**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 x2 = –1, the only solution is 0.

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**Polynomial equations can also be solved numerically and graphically.**

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Example Solve the equation 6x – x2 = 0 numerically, graphically, and symbolically. Solution Numerical: Make a table of values. x y 1 7 1 5 2 8 3 9 4 6 Graphical: Plot the points in the table. The intercepts are the solution to the equation.

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Example (cont) Solve the equation 6x – x2 = 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.

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Example Factor. a. 3x(x + 1) + 4(x + 1) b. 3x2(2x – 1) – x(2x – 1) Solution a. Both terms in the expression contain the binomial x + 1. Use the distributive property to factor. b.

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Example Factor the polynomial. Solution

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Example Factor the polynomial. Solution

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