Section 3: Zeros of the Quadratic

# Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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462 Chapter 5 Quadratic Functions Version: Fall 2007 Thus, our factorization is correct. Let’s summarize the technique. Algorithm. To factor the quadratic x 2 + bx + c , proceed as follows: 1. List all the integer pairs whose product equals c . 2. Circle or frame the pair whose sum equals the coefficient of x , namely b . Use this pair to factor the trinomial. Let’s look at another example. l⚏ Example 2. Factor the trinomial x 2 25 x 84 . List all the integer pairs whose product is 84 . 1 , 84 1 , 84 2 , 42 2 , 42 3 , 28 3 , 28 4 , 21 4 , 21 6 , 14 6 , 14 7 , 12 7 , 12 We’ve framed the pair whose sum equals the coefficient of x , namely 25 . Use this pair to factor the trinomial. x 2 25 x 84 = ( x + 3)( x 28) Check. ( x + 3)( x 28) = x ( x 28) + 3( x 28) = x 2 28 x + 3 x 84 = x 2 25 x 84 With experience, there are a number of ideas that will quicken the process.
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