1. By addisonwagner Math Chapter 6.3 Tutorial

2. Objective Using the grouping method to factor trinomials in the form of There is an alternative method that can be used to factor trinomials of the form . This method is called the grouping method because it uses factoring by grouping as we learned in Section 6.1. To see how this method works, recall from Section 6.1 that to factor a trinomial such as we find two numbers that have the product of 30 and the sum of 11.

3. Continued… To factor trinomials such as by grouping, we use an extension of the method in Section 6.1. Here we look for two numbers such that the product is 2 4 and the sum is 11. This time we use numbers to write Then we factor by grouping. Since we want a positive product, 24, and a positive sum, 11, we consider pairs of positive factors of 21 only.  

4. Continued… The factors are 3 and 8. Now we use these factors to write the middle term 11x as 3x+8x (or 8x + 3x). We replace 11x with 3x+8x in the original trinomial and then we can factor by grouping.  + Group the terms. Factor each group. Factor out (2x+3).

5. Step 1. Factor out the greatest common factor, if there is one other then 1. Step 2. For the resulting trinomial , find two numbers whose product is and whose sum is b. Step 3. Write the middle term, bx, using the factors found in step 2. Step 4. Factor by grouping. STEPS TO FACTOR TRINOMIALS BY GROUPING

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