algebra 2 4.4

Slide 1: 

Find the product 1. (4y – 3)(3y + 8) 2. (5m + 6)(5m – 6) 12y2 + 23y – 24 25m2 – 36 3. (4q – 5)2 16q2 – 40q + 25 4. Solve x2 – x – 30 = 0. (x – 6 )(x + 5) = 0 x = 6 or x = -5 Bell Ringer WarmUps

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

Slide 4: 

GUIDED PRACTICE for Examples 1 and 2 GUIDED PRACTICE Factor the expression. If the expression cannot be factored, say so. 1. 7x2 – 20x – 3 2. 5z2 + 16z + 3 3. 2w2 + w + 3 cannot be factored Factors of -21 that add up to -20 -21 and 1 (7x )(x ) – 3 + 1 Factors of 15 that add up to 16 15 and 1 (5z )(z ) + 3 + 1 Factors of 6 that add up to 1 There are none 4. 3x2 + 5x – 12 Factors of -36 that add up to 5 9 and -4 (3x )(x ) + 3 – 4

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GUIDED PRACTICE for Examples 1 and 2 GUIDED PRACTICE 5. 4u2 + 12u + 5 6. 4x2 – 9x + 2 Factors of 20 that add up to 12 10 and 2 (2u )(2u ) + 5 + 1 Factors of 8 that add up to -9 -8 and -1 (4x )(x ) – 2 – 1 (4u )(u ) (2x )(2x )

Slide 6: 

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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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. 36w2 – 12w + 1 = (6w – 1)2 Perfect square trinomial

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

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

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

Homework 4.4 : 

Homework 4.4 Pages: 263 – 265 Exs. 4 – 20 even, 24, 28, 32, 36, 40, 44, 48, 54, 69, 70