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Warm up #5: Factor Completely. y 2 + 7y +12 2x 2 + 7x + 3 3m 2 – m – 4 6t 2 + 23t + 7 5k 2 + k –18. Wu #3: Factor Completely. (y + 3)(y + 4). (x + 3)(2x + 1). y 2 + 7y +12 2x 2 + 7x + 3 3m 2 – m – 4 6t 2 + 23t + 7 5k 2 + k –18. (m + 1)(3m - 4). (2y + 7)(3t + 1).
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Warm up #5: Factor Completely • y2 + 7y +12 • 2x2 + 7x + 3 • 3m2 – m – 4 • 6t2 + 23t + 7 • 5k2 + k –18
Wu #3: Factor Completely (y + 3)(y + 4) (x + 3)(2x + 1) • y2 + 7y +12 • 2x2 + 7x + 3 • 3m2 – m – 4 • 6t2 + 23t + 7 • 5k2 + k –18 (m + 1)(3m - 4) (2y + 7)(3t + 1) (k + 2)(5k - 9) Good Job!!
6.6 Factor by Grouping • Goal: To be able to factor polynomials with 4 terms by grouping
When…… • When does it work? Always • When should I use it? For any polynomial but especially when you have 4 or more terms.
Steps • Put ( ) around first 2 terms and last 2 terms • Factor out a common factor so what is left in the binomials is the same • Make the numbers you factored out into a binomial and multiply it by 1 of the same binomials
Factoring by Grouping + Use when there are 4 Terms 6x3 – 9x2 + 4x - 6 3x2(2x – 3) 2(2x – 3) (2x – 3) ( 3x2 + 2)
Factoring by Grouping + Use when there are 4 Terms x3 + x2 + x + 1 x2( x + 1) 1( x + 1) (x + 1) ( x2 + 1)
Factoring by Grouping - Use when there are 4 Terms x3 + 2x2 - x - 2 x2( x + 2) 1( x + 2) (x + 2) ( x2 - 1) ( x - 1)(x + 1) (x + 2)
Factor completely if possible…8x3 + 2x2 + 12x +3 (4x + 1)(2x2 + 3)
Factor completely if possible…4x3 - 6x2 - 6x + 9 (2x - 3)(2x2 - 3)
Factor completely if possible…4x3 - 6x2 - 6x + 9 (2x - 3)(2x2 - 3)
