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9.8 Factoring by Grouping

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9.8 – Factor by Grouping Goals / “I can…” Factor polynomials with 4 terms Factor trinomials by grouping

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9.8 – Factor by Grouping Look at the following: 5t + 20t + 6t + 24 I can’t factor a fourth power. 43

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9.8 – Factor by Grouping BUT try grouping the terms together (5t + 20t ) + (6t + 24) Can I factor something in the first parentheses? The second? 43

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9.8 – Factor by Grouping 5t (t + 4)+ 6(t + 4) Notice, both have a (t + 4) SO… 3

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9.8 – Factor by Grouping (5t + 6)(t + 4) 3

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Factor by Grouping Example 1: 3xy - 21y + 5x – 35 FACTOR: 3xy - 21y + 5x – 35 Factor the first two terms: 3xy - 21y = 3y (x – 7) Factor the last two terms: + 5x - 35 = 5 (x – 7) The blue parentheses are the same so it’s the common factor Now you have a common factor (x - 7) (3y + 5)

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Factor by Grouping Example 2: 6mx – 4m + 3rx – 2r FACTOR: 6mx – 4m + 3rx – 2r Factor the first two terms: 6mx – 4m = 2m (3x - 2) Factor the last two terms: + 3rx – 2r = r (3x - 2) The blue parentheses are the same so it’s the common factor Now you have a common factor (3x - 2) (2m + r)

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Factor by Grouping Example 3: 15x – 3xy + 4y –20 FACTOR: 15x – 3xy + 4y –20 Factor the first two terms: 15x – 3xy = 3x (5 – y) Factor the last two terms: + 4y –20 = 4 (y – 5) The green parentheses are opposites so change the sign on the 4 - 4 (-y + 5) or – 4 (5 - y) Now you have a common factor (5 – y) (3x – 4)

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9.8 – Factor by Grouping TRY: 6x + 3x – 4x – 2 32

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9.8 – Factor by Grouping TRY: 4n + 8n - 5n – 10 32

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9.8 – Factor by Grouping TRY: 12p + 10p - 36p – 30p 43 2

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9.8 – Factor by Grouping

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You may have to rearrange the terms 1 st

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Now let’s try it with 3 terms Can we still group these? 6x + 5x + 1 2

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9.6 – Factoring Trinomials TRY: 6y + 23y + 7 2

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9.6 – Factoring Trinomials TRY: 7y - 26y - 8 2

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9.6 – Factoring Trinomials Look at the trinomial: 20y + 17y + 3 2

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9.6 – Factoring Trinomials TRY: 3y – 16y – 12 2

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9.6 – Factoring Trinomials TRY: 24y + 10y - 6 2

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