1. Example 1 b and c Are Positive
Example 2 b Is Negative and c Is Positive
Example 3 b Is Positive and c Is Negative
Example 4 b Is Negative and c Is Negative
Example 5 Solve an Equation by Factoring
Example 6 Solve a Real-World Problem by Factoring
Lesson 3 Contents

2. Example 1
b and c Are Positive

3. Factor
In this trinomial, and You need to find the two numbers whose sum is 7 and whose product is 12.
Factors of 12
Sum of Factors
1, 12 2, 6 3, 4
13 8 7
The correct factors are 3 and 4.
Answer:
and
Example 3-1a

4. Check You can check the result by multiplying the two factors.
FOIL method F O I L
Simplify.
Example 3-1a

5. Factor
Answer:
Example 3-1b

6. b Is Negative and c Is Positive
Example 2
b Is Negative and c Is Positive

7. Factor
In this trinomial, and This means is negative and mn is positive. So m and n must both be negative. Therefore, make a list of the negative factors of 27, and look for the pair whose sum is –12.
Factors of 27
Sum of Factors
–1, –27 –3, –9
–28 –12
The correct factors are –3 and –9.
Answer:
and
Example 3-2a

8. Factor
Answer:
Example 3-2b

9. b Is Positive and c Is Negative
Example 3
b Is Positive and c Is Negative

10. The correct factors are –3 and 6.
In this trinomial, and This means is positive and mn is negative, so either m or n is negative, but not both. Therefore, make a list of the factors of –18 where one factor of each pair is negative. Look for the pair of factors whose sum is 3.
Factors of –18
Sum of Factors
1, –18 –1, , –9 –2, , –6 –3, 6
– – –
The correct factors are –3 and 6.
Example 3-3a

11. Answer:
and
Example 3-3a

12. Factor
Answer:
Example 3-3b

13. b Is Negative and c Is Negative
Example 4
b Is Negative and c Is Negative

14. Factor
Since and is negative and mn is negative. So either m or n is negative, but not both.
Factors of –20
Sum of Factors
1, –20 –1, , –10 –2, , –5 –4, 5
– – –
The correct factors are 4 and –5.
Example 3-4a

15. Answer:
and
Example 3-4a

16. Factor
Answer:
Example 3-4b

17. Solve an Equation by Factoring
Example 5
Solve an Equation by Factoring

18. Rewrite the equation so that one side equals 0.
Solve
Check your solutions.
Original equation
Rewrite the equation so that one side equals 0.
Factor. or
Zero Product Property
Solve each equation.
Answer: The solution is
Example 3-5a

19. Check Substitute –5 and 3 for x in the original equation.
Example 3-5a

20. Solve
Check your solutions.
Answer:
Example 3-5b

21. Your Reward
Pages even

22. End of Lesson 3