4.4 Factoring Trinomials by Grouping BobsMathClass.Com Copyright © 2010 All Rights Reserved. 1 Factor out a 3x from the first pair. Since the first term of the second pair is negative, factor out a –2y. Lastly, factor out the common binomial. There are a few different approaches for factoring trinomials. The grouping method, also called the ‘ac’ method is the method we will use in this lesson. Recall the process of factoring by grouping: To factor trinomials we will need to “split” a term into two terms using a specific pair of numbers. For example: If we want –13x from an 8 and 5, both signs will be negative. –8x – 5x = –13x Suppose we want –2x from an 6 and 8, the 6 would have to be positive and the 8 negative. –8x + 6x = –2x or +6x – 8x = –2x (order does not matter) How would we get –6x from 3 and 9? +3x – 9x = –6x or –9x + 3x = –6x

4.4 Factoring Trinomials by Grouping BobsMathClass.Com Copyright © 2010 All Rights Reserved Multiply a and c. List the factors. 2. Find pair that subtracts to equal middle #. 3. Separate middle term into two terms using the numbers from step 2. The order does not matter. 4. Now factor by grouping. 3. Then, separate the middle term into two terms with the pair found. Use the appropriate signs so the value is not changed. 4. Now factor by grouping. 2. If the last sign is negative, find the pair which will subtract to equal the middle #. If the last sign is positive, find the pair which will add to equal the middle #. 1. Multiply the first and last number (a  c). Then list all the factors of the result. Don’t worry about the sign at this point. Procedure for Factoring Trinomials by Grouping 5. Check by the Multiplying (FOIL) 5. Check by FOIL

4.4 Factoring Trinomials by Grouping BobsMathClass.Com Copyright © 2010 All Rights Reserved. 3 Your Turn Problem #1 2. Find pair that subtracts to equal middle #. 3. Separate middle term into two terms using the numbers from step 2. The order does not matter. 4. Now factor by grouping. 5. Check by FOIL (Not Shown) Notice the first term of the second pair is a negative (-15x). Since it is a negative, we need to factor it out along with the gcf, which is –3. Also notice the parentheses match. If they do not match, we’re messing up somewhere. 1. Multiply a and c. List the factors.

4.4 Factoring Trinomials by Grouping BobsMathClass.Com Copyright © 2010 All Rights Reserved Multiply a and c. List the factors. 2. Find pair that adds to equal middle #. 3. Separate middle term into two terms using the numbers from step 2. The order does not matter. 4. Now factor by grouping. Your Turn Problem #2 5. Check by FOIL (Not Shown)

4.4 Factoring Trinomials by Grouping BobsMathClass.Com Copyright © 2010 All Rights Reserved. 5 Your Turn Problem #3 1. Multiply a and c. List the factors. 2. Find pair that subtracts to equal middle #. 3. Separate middle term into two terms using the numbers from step 2. The order does not matter. 4. Now factor by grouping. 5. Check by FOIL (Not Shown)

4.4 Factoring Trinomials by Grouping BobsMathClass.Com Copyright © 2010 All Rights Reserved. 6 Your Turn Problem #4 1. Arrange the trinomial in descending order. 3. Factor the remaining trinomial or binomial if possible. Write gcf in front of this factorization. General Steps for Factoring Trinomials 2. Factor out the gcf. If the first term is negative, factor out the negative along with the gcf. 4. Check by the Multiplying (FOIL) 1. Arrange in descending order. 2. Factor out the gcf. 3. Factor the trinomial using the grouping method.

4.4 Factoring Trinomials by Grouping BobsMathClass.Com Copyright © 2010 All Rights Reserved. 7 Your Turn Problem #5 1. Arrange in descending order. 2. Factor out the negative. 3. Factor the trinomial using the grouping method.

4.4 Factoring Trinomials by Grouping BobsMathClass.Com Copyright © 2010 All Rights Reserved. 8 Your Turn Problem #6 1. Already in descending order and there is no gcf. 2. When separating the middle term, the variable part will be xy.

4.4 Factoring Trinomials by Grouping BobsMathClass.Com Copyright © 2010 All Rights Reserved. 9 Not all trinomials can be factored. If this is the case, the answer to be written is “The trinomial is not factorable.” 2. Which pair will subtract to equal 8? Answer: None? Therefore, the trinomial is not factorable. Your Turn Problem #7 1. Multiply a and c. List the factors.

4.4 Factoring Trinomials by Grouping BobsMathClass.Com Copyright © 2010 All Rights Reserved. 10 Your Turn Problem #8 We can still use the factoring by grouping technique for these trinomials. When we “split” the middle term, the variable part must remain the same, x 2. Multiply a and c. List the factors. This one does have quite a few factors. We really just need to find the pair that subtracts to equal the middle #. The End