# Factoring Trinomials Contributed by: OBJECTIVE:
1. Factor trinomials when the coefficient of the squared term is 1. 2. Factor trinomials when the coefficient of the squared term is not 1. 3. Use an alternative method of factoring trinomials. 4. Factor by substitution.
Sec 7.2 - 1
2. Chapter 7
Factoring
Sec 7.2 - 2
3. 7.2
Factoring Trinomials
Sec 7.2 - 3
4. 7.2 Factoring Trinomials
Objectives
1. Factor trinomials when the coefficient of
the squared term is 1.
2. Factor trinomials when the coefficient of
the squared term is not 1.
3. Use an alternative method of factoring
trinomials.
4. Factor by substitution.
5. 7.2 Factor Trinomials
Factor Out the Greatest Common Factor
The product of two binomials sometimes gives a trinomial. For
example:
So, we have two processes that “undo” each other.
Multiplying
Factored form Product
Factoring
6. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient of the Squared Term is 1
Multiplying binomials uses the FOIL method, and factoring
involves using the FOIL method backwards.
2
Product of x and x is x.
F
L Product of 5 and –7 is –35.
Sum of the product of outer and inner terms
O I
7. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is 1
8. 7.2 Factor Trinomials
Factoring Trinomials in Form
Step 1 Step 2
Coefficient
of middle
term
9. 7.2 Factor Trinomials
Factoring Trinomials in Form
The required numbers are –8 and 4, so
factors to see if you get the original polynomial.
Guidelines for Factoring Trinomials
1. If the last term is positive, the factors will have the form
( ___ + ___ ) ( ___ + ___ ) or ( ___ – ___ ) ( ___ – ___ )
The + or – sign is determined by the coefficient of the middle term.
2. If the last term is negative, the factors will have the form
( ___ + ___ ) ( ___ – ___ ) or ( ___ – ___ ) ( ___ + ___ )
10. 7.2 Factor Trinomials
Factoring a Trinomial With A Common Factor
11. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
12. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
13. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Listing all the pairs of
numbers whose product
is –24 to find a pair
whose sum is –10, only
2 and –12 have a sum of
14. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
15. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Factoring Other Trinomials by Trial and Error
16. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Factoring Other Trinomials by Trial and Error
17. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Factoring Other Trinomials by Trial and Error
Here are the possibilities, each of which produces the correct
first and last term, 3x2 and –2, respectively.
18. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Trial and Error (Alternative Method) Summarized
19. 7.2 Factor Trinomials