Example 1 b and c Are Positive

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Presentation transcript:

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

Example 1 b and c Are Positive

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

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

Factor Answer: Example 3-1b

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

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

Factor Answer: Example 3-2b

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

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, 18 2, –9 –2, 9 3, –6 –3, 6 –17 17 – 7 7 – 3 3 The correct factors are –3 and 6. Example 3-3a

Answer: and Example 3-3a

Factor Answer: Example 3-3b

b Is Negative and c Is Negative Example 4 b Is Negative and c Is Negative

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, 20 2, –10 –2, 10 4, –5 –4, 5 –19 19 – 8 8 – 1 1 The correct factors are 4 and –5. Example 3-4a

Answer: and Example 3-4a

Factor Answer: Example 3-4b

Solve an Equation by Factoring Example 5 Solve an Equation by Factoring

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

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

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

Your Reward Pages 493 18-52 even

End of Lesson 3