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Published byRhoda Madison Green Modified over 8 years ago

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**Lesson 9.3 Factoring Trinomials: x² + bx + c**

Objectives: To factor trinomials of the form x² + bx + c To solve equations of the form x²+ bx + c = 0

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**Factoring x² + bx + c (x + )(x + )**

To factor a trinomial of the form x² + bx + c find two numbers with the sum of the middle term b and product of the last term c. Example: x² + 11x + 24 Factors of 24 Sum of 11 sum of 11 product of 24 (x + )(x + ) Note: X² will always factor into x and x

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**Ex. 1: Factor each trinomial.**

x² + 7x + 12 2. x² - 12x + 27

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3. x² + 3x - 18 4. x² - x - 20

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a + a² 6. x² - 4xy + 3y²

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Your turn…… p² - 2p – 35 h² + 3h - 40 c² - 3c + 2 c² + 12c + 35

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Some equations of the form x² + bx + c = 0 can be solved by factoring and then using the Zero Product Property.

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**Ex. 2: Solve each equation.**

1. x² + 16x + 28 = 0 2. y² + 4y – 12 = 0

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3. z² = z 4. c² - 50 = -23c

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Your turn… 5. x² + 2x = 15 6. 14p + p² = 51

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**SUMMARY To factor a trinomial of the form x² + bx + c**

find two numbers with the sum of the middle term b and product of the last term c. To solve an equation of the form x² + bx + c = 0, set the equation equal to zero, factor, and use the Zero Product Property to solve. NBA #3, page 493, problems even

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