Warm-Up # A park is in the shape of a rectangle 8 miles long and 6 miles wide. How much shorter is your walk if you walk diagonally across the park than.

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Presentation transcript:

Warm-Up # A park is in the shape of a rectangle 8 miles long and 6 miles wide. How much shorter is your walk if you walk diagonally across the park than along two sides of it? The bases on a softball diamond are 60 feet apart. How far is it from home plate to second base? Expand it out: f(x) = -2(x + 1) (x -7)

Homework Lesson 5.3_page 296 #30-48 even

Golden Rules of Factoring

Example: Factor out the greatest common factor f(x)= 4x2 + 20x -12

Practice: Factor each expression Solutions: a.) 3(3x2 + x – 6) b) 7(p2 + 3) c) 2w(2w + 1) a) f(x)= 9x2 + 3x – 18 b) f(x)= 7p2 + 21 c) f(x)= 4w2 + 2w

Factor Diamonds f(x)=1x² + 8x + 7 (x + 1) (x + 7) ac add multi b 7 7 1

Practice: Solve by a factor diamond 1) x2 + 15x + 36 2) x2 - 56 -10x

Factor by Grouping f(x)= 2x² – 7x – 15 2x² – 10x + 3x – 15 =0 -30 -10 3 -7 Note: you are on the right track because you have (x-5) in both parenthesis 2x(x – 5) + 3(x – 5) =0 (2x + 3)(x – 5)=0

Practice: Factor by Grouping f(x)= 3x2 + 7x – 20 2) f(x)= 3x2 - 5x – 2

SHORTCUTS a2 + 2ab + b2 (a+b)2 a2 - 2ab + b2 (a - b)2 Example: 25x2 + 90x + 81 (5x + 9)2 a2 - 2ab + b2 (a - b)2 Example: 9x2 – 42x + 49 (3x – 7)2 a2 - b2 (a+b)(a - b) Example: x2 – 64 (x + 8)(x – 8)

Practice Problems: Solve using any method Solutions: a) (x-6)(3x+2) (x+2)(4x-3) (2x+7)(2x-7) (x+4)(2x+3) f(x)= 3x2 – 16x – 12 f(x)= 4x2 + 5x – 6 f(x)= 4x2 – 49 f(x)= 2x2 + 11X + 12