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Published byMartin Neal Modified over 9 years ago

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**Warm Up #8 Find the product 2. (5m + 6)(5m – 6) 1. (4y – 3)(3y + 8)**

3. (4q – 5)2 4. Solve x2 – x – 30 = 0. 16q2 – 40q + 25 (x – 6 )(x + 5) = 0 x = 6 or x = -5

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EXAMPLE 1 Factor 5x2 – 17x + 6. Factors of +30 That add up to -17 (5x )(x ) – 2 – 3 -15 and -2 Factor 3x2 + 20x – 7. Factors of -21 That add up to + 20 (3x )(x ) – 1 + 7 21 and -1

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**GUIDED PRACTICE GUIDED PRACTICE for Examples 1 and 2 1. 7x2 – 20x – 3**

Factor the expression. If the expression cannot be factored, say so. x2 – 20x – 3 z2 + 16z + 3 Factors of -21 that add up to -20 Factors of 15 that add up to 16 -21 and 1 15 and 1 (7x )(x ) + 1 – 3 (5z )(z ) + 1 + 3 x2 + 5x – 12 w2 + w + 3 Factors of -36 that add up to 5 Factors of 6 that add up to 1 9 and -4 There are none cannot be factored (3x )(x ) – 4 + 3

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**GUIDED PRACTICE GUIDED PRACTICE for Examples 1 and 2 6. 4x2 – 9x + 2**

u2 + 12u + 5 Factors of 20 that add up to 12 Factors of 8 that add up to -9 10 and 2 -8 and -1 (4u )(u ) (4x )(x ) – 1 – 2 (2u )(2u ) + 1 + 5 (2x )(2x )

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**Recall: x2 – y2 = (x – y)(x + y)**

Example: 4x2 – 25 = (2x – 5)(2x + 5) Recall: x2 + 2xy + y2 = (x + y)2 Example: 9x2 + 30x + 25 = (3x + 5)2

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**Factor with special patterns**

EXAMPLE 3 Factor with special patterns Factor the expression. a. 9x2 – 64 = (3x – 8)(3x + 8) Difference of two squares b. 4y2 + 20y + 25 = (2y + 5)2 Perfect square trinomial c w2 – 12w + 1 = (6w – 1)2 Perfect square trinomial

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EXAMPLE 4 Recall: GCF (Greatest Common Factor) Factor the expression. a. 5x2 – 45 = 5(x2 – 9) = 5(x + 3)(x – 3) b. 6q2 – 14q + 8 = 2(3q2 – 7q + 4) = 2(3q – 4)(q – 1) c. –5z2 + 20z = –5z(z – 4) d. 12p2 – 21p + 3 = 3(4p2 – 7p + 1)

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**Solve quadratic equations**

EXAMPLE 5 Solve quadratic equations Solve (a) 3x2 + 10x – 8 = 0 a. 3x2 + 10x – 8 = 0 Write original equation. Factors of -24 that add up to 10 Factor. 12 and -2 (3x )(x ) = 0 – 2 + 4 3x – 2 = 0 or x + 4 = 0 Zero product property 3x = 2 Solve for x. or x = –4 x = 23

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**Solve quadratic equations**

EXAMPLE 5 Solve quadratic equations (b) 5p2 – 16p + 15 = 4p – 5. b. 5p2 – 16p + 15 = 4p – 5. Write original equation. 5p2 – 20p + 20 = 0 Write in standard form. 5(p2 – 4p + 4) = 0 Factor out a 5. p2 – 4p + 4 = 0 Divide each side by 5. (p – 2)2 = 0 Factor. p – 2 = 0 Zero product property p = 2 Solve for p.

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