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9.8

9.8. Factoring by Grouping. 9.8 – Factor by Grouping. Goals / “I can…” Factor polynomials with 4 terms Factor trinomials by grouping. 9.8 – Factor by Grouping. Look at the following: 5t + 20t + 6t + 24 I can’t factor a fourth power. 4. 3. 9.8 – Factor by Grouping.

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9.8

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  1. 9.8 Factoring by Grouping

  2. 9.8 – Factor by Grouping • Goals / “I can…” • Factor polynomials with 4 terms • Factor trinomials by grouping

  3. 9.8 – Factor by Grouping • Look at the following: 5t + 20t + 6t + 24 • I can’t factor a fourth power. 4 3

  4. 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? 4 3

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

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

  7. Factor by GroupingExample 1: • 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)

  8. Factor by GroupingExample 2: • 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)

  9. Factor by GroupingExample 3: • 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 the4 - 4(-y + 5) or – 4(5 - y) • Now you have a common factor (5 – y)(3x – 4)

  10. 9.8 – Factor by Grouping • TRY: 6x + 3x – 4x – 2 3 2

  11. 9.8 – Factor by Grouping • TRY: 4n + 8n - 5n – 10 3 2

  12. 9.8 – Factor by Grouping • TRY: 12p + 10p - 36p – 30p 2 4 3

  13. 9.8 – Factor by Grouping

  14. 9.8 – Factor by Grouping

  15. 9.8 – Factor by Grouping • You may have to rearrange the terms 1st

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

  17. 9.6 – Factoring Trinomials • TRY: 6y + 23y + 7 2

  18. 9.6 – Factoring Trinomials • TRY: 7y - 26y - 8 2

  19. 9.6 – Factoring Trinomials • Look at the trinomial: 20y + 17y + 3 2

  20. 9.6 – Factoring Trinomials • TRY: 3y – 16y – 12 2

  21. 9.6 – Factoring Trinomials • TRY: 24y + 10y - 6 2

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