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Q&A #104

Teachers' Lounge Discussion: Factoring trinomials

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From: Thunder <mrsbinsta@yahoo.com>
To: Teacher2Teacher Public Discussion
Date: 2002090221:48:53
Subject: Factoring    35x^2-88x+45

To factor  35x^2 - 88x + 45

List the factors of the 'a' term vertically:
 1  5  7  35
35  7  5   1

List the factors of the 'c' term vertically:
 1   3   5
45  15   9

Now cross multiply each set of 'a' factors with each set of 'c'
factors. Since 'c' is positive, you ADD these two products to find the
sum of 88. I use a giant T to visualize. (If 'c' were negative, you
would SUBTRACT the two products.)

     a = 35   |   c = 45
--------------|-------------
 1  5  7  35  |  1   3   5
35  7  5   1  | 45  15   9  
                                 -----|-----
In this case we use the factors:   7  |  5
                                   5  |  9

7 x 9 = 63
5 x 5 = 25
       ----
        88

Now you read the factors across the T as such:
(7x - 5)(5x - 9)

Since the 'b' term is negative, the second term in each binomial is
also negative.

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