After studying this lesson, you will be able to: - Factor trinomials.
1. Factor out the GCF 2. Look at the number of terms: - 2 Terms: Look for the Difference of 2 Squares
- 3 Terms: Factor the Trinomial
- 4 Terms: Factor by Grouping
3. Factor Completely 4. Check by Multiplying This lesson will concentrate on the second step of factoring:Factoring Trinomials. **When there are 3 terms, we are factoring trinomials. Don'tforget to look for a GCF first.** Factoring trinomials often requires some trial and error.Don't get frustrated. Try all possible combinations.
## Rules for determining the signs in each factor:
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Factor x This is a trinomial (has 3 terms). There is no GCF other thanone. So, we start with 2 parentheses: Using our signs rules, we can determine the signs for thefactors. Since the constant term is positive we know the signswill be the same. Since we want the factors to add up to +7xy thesigns will both have to be positive. Keep this in mind. 1 st : Find the factors of the first term. The factors of x 2 nd : Find the factors of the constant term. The factors of10y (x + 2y ) ( x + 5y) Check by using FOIL (x + 2y) (x + 5y)
Factor x This is a trinomial (has 3 terms). There is no GCF other thanone. So, we start with 2 parentheses: Using our signs rules, we can determine the signs for thefactors. Since the constant term is negative we know the signswill be different. We want the factors to add up to -8x. Let'sremember that the signs are different. We aren't sure just yetwhich sign will be positive and which will be negative. 1 st : Find the factors of the first term. The factors of x 2are x and x. These go in the first positions. We don't yet put inthe signs because we aren't sure where they go. 2 nd : Find the factors of the constant term. The factors of20 are 1, 20 and 2, 10 and 4, 5. Remember, we need theinside/outside combination to add up to the middle term which is-8x. We have to remember that we are working with differentsigns. Therefore, we're really looking for a pair of factors thathave a difference of 8. Since 2 and 10 have a difference of 8, wechoose those factors. Now we have to decide where to put thepositive and where to put the negative. The 2 and the 10 have toadd up to -8 so we make the 10 negative and the 2 positive. (x + 2 ) ( x - 10 ) Check by using FOIL (x + 2) ( x - 10 )
Factor x This is a trinomial (has 3 terms). There is no GCF other thanone. So, we start with 2 parentheses: Using our signs rules, we can determine the signs for thefactors. Since the constant term is negative we know the signswill be different. We want the factors to add up to +4x. Let'sremember that the signs are different. We aren't sure just yetwhich sign will be positive and which will be negative. 1st : Find the factors of the first term. The factors of x 2are x and x. These go in the first positions. We don't yet put inthe signs because we aren't sure where they go. 2 nd : Find the factors of the constant term. The factors of12 are 1, 12 and 2, 6 and 3, 4. Remember, we need theinside/outside combination to add up to the middle term which is-+4x. We have to remember that we are working with differentsigns. Therefore, we're really looking for a pair of factors thathave a difference of 4. Since 2 and 6 have a difference of 4, wechoose those factors. Now we have to decide where to put thepositive and where to put the negative. The 2 and the 6 have toadd up to +4 so we make the 2 negative and the 6 positive. (x - 2 ) ( x + 6 ) note : it would be the same thing to writethe factors in this order: (x - 6) (x - 2 ) Check by using FOIL (x - 2) ( x + 6 ) |