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Section 13.4 factoring trinomials using the foil method

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Section 13.4 Factoring Trinomials Using the Foil Method

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Slide - 1Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G 2 Factoring and Applications 13
Slide - 2Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G 1. Factor trinomials by using the FOIL method. Objectives 13.4 Factoring Trinomials by Using the FOIL Method
Slide - 3Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Note If the original polynomial has no common factor, then none of its binomial factors will either. Factoring Trinomials Using FOIL
Slide - 4Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor 18p2 + 13p + 2. Add. ( + 1 ) ( + 2 )18p p 36p 1p 37p Add. ( + 1 ) ( + 2 )p 18p 2p 18p 20p Add. ( + 1 ) ( + 2 )9p 2p 18p 2p 20p Add. ( + 1 ) ( + 2 )2p 9p 4p 9p 13p Check by multiplying. Factor Trinomials Using FOIL Example Look for a sum of +13p.
Slide - 5Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor 28g2 + 39g + 5. Add. ( + 1 ) ( + 5 )28g g 140g 1g 141g Add. ( + 1 ) ( + 5 )g 28g 5g 28g 33g Add. ( + 1 ) ( + 5 )14g 2g 70g 2g 72g Add. ( + 1 ) ( + 5 )2g 14g 10g 14g 24g Factor Trinomials Using FOIL Example Look for a sum of +39g.
Slide - 6Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor 28g2 + 39g + 5. Add. ( + 1 ) ( + 5 )7g 4g 35g 4g 39g Check by multiplying. Factor Trinomials Using FOIL Example (cont.) Look for a sum of +39g.
Slide - 7Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example Factor 8n2 – 10n + 3. Add. ( – 1 ) ( – 3 )8n n –24n –1n –25n Add. ( – 1 ) ( – 3 )n 8n –3n –8n –11n Add. ( – 1 ) ( – 3 )4n 2n –12n –2n –14n Add. ( – 1 ) ( – 3 )2n 4n –6n –4n –10n Check by multiplying.Look for a sum of –10n.
Slide - 8Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example Factor 10k2 – 19k + 7. Add. ( – 1 ) ( – 7 )10k k –70k –1k –71k Add. ( – 1 ) ( – 7 )k 10k –7k –10k –17k Add. ( – 1 ) ( – 7 )5k 2k –35k –2k –37k Add. ( – 1 ) ( – 7 )2k 5k –14k –5k –19k Check by multiplying.Look for a sum of –19k.
Slide - 9Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example Factor 36d 2 + 4d – 7. Add. ( + 1 ) ( – 7 )36d d –252d 1d –251d Add. ( + 1 ) ( – 7 )d 36d – 7d 36d 29d Add. ( – 1 ) ( + 7 )36d d 252d –1d 251d Add. ( – 1 ) ( + 7 )d 36d 7d –36d –29d Look for a sum of +4d.
Slide - 10Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example (cont.) Factor 36d 2 + 4d – 7. Add. ( + 1 ) ( – 7 )18d 2d –126d 2d –124d Add. ( + 1 ) ( – 7 )2d 18d – 14d 18d 4d Check by multiplying.Look for a sum of +4d.
Slide - 11Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomial Using FOIL Example Factor 15a2 + 7a – 4. Add. ( + 1 ) ( – 4 )15a a –60a 1a –59a Add. ( + 1 ) ( – 4 )a 15a – 4a 15a 11a Add. ( – 1 ) ( + 4 )15a a 60a –1a 59a Add. ( – 1 ) ( + 4 )a 15a 4a –15a –11a Look for a sum of +7a.
Slide - 12Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomial Using FOIL Example (cont.) Factor 15a2 + 7a – 4. Add. ( + 1 ) ( – 4 )5a 3a –20a 3a –17a Add. ( + 1 ) ( – 4 )3a 5a –12a 5a –7a Add. ( – 1 ) ( + 4 )5a 3a 20a –3a 17a Add. ( – 1 ) ( + 4 )3a 5a 12a –5a 7a Check by multiplying.Look for a sum of +7a.
Slide - 13Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example Add. ( + 7y ) ( – 5y )3x 4x –15xy 28xy 13xy Look for a sum of –13xy.Factor 12x2 – 13xy – 35y2 Add. ( + 7y ) ( – 5y )4x 3x –20xy 21xy 1xy Add. ( – 7y ) ( + 5y )3x 4x 15xy –28xy –13xy Check by multiplying.
Slide - 14Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Check by multiplying. Factor Trinomials Using FOIL Example Add. ( + 5b ) ( – 3b )8a 3a –24ab 15ab –9ab Look for a sum of +2ab.Factor 24a2 + 2ab – 15b2. Add. ( + 5b ) ( – 3b )3a 8a –9ab 40ab 31ab Add. ( + 5b ) ( – 3b )6a 4a –18ab 20ab 2ab
Slide - 15Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example Add. ( + 5 ) ( + 2 )6y 3y 12y 15y 27y Check by multiplying.Look for a sum of +27y.Factor 90y3 + 135y2 + 50y. 90y3 + 135y2 + 50y = 5y (18y2 + 27y + 10) The completely factored form of 90y3 + 135y2 + 50y is 90y3 + 135y2 + 50y = 5y (6y + 5) (3y + 2)
Slide - 16Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example Add. ( – 3 ) ( – 2 )7x 2x –14x –6x –20x Check by multiplying.Look for a sum of –25x.Factor 42x3 – 75x2 + 18x. 42x3 – 75x2 + 18x = 3x (14x2 – 25x + 6) Add. ( – 3 ) ( – 2 )2x 7x –4x –21x –25x The completely factored form of 42x3 – 75x2 + 18x is 42x3 – 75x2 + 18x = 3x (2x – 3) (7x – 2)
Slide - 17Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Remember to include the common factor in the final factored form. CAUTION Factor Trinomials Using FOIL

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Section 13.4 factoring trinomials using the foil method

  • 1. Slide - 1Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G 2 Factoring and Applications 13
  • 2. Slide - 2Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G 1. Factor trinomials by using the FOIL method. Objectives 13.4 Factoring Trinomials by Using the FOIL Method
  • 3. Slide - 3Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Note If the original polynomial has no common factor, then none of its binomial factors will either. Factoring Trinomials Using FOIL
  • 4. Slide - 4Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor 18p2 + 13p + 2. Add. ( + 1 ) ( + 2 )18p p 36p 1p 37p Add. ( + 1 ) ( + 2 )p 18p 2p 18p 20p Add. ( + 1 ) ( + 2 )9p 2p 18p 2p 20p Add. ( + 1 ) ( + 2 )2p 9p 4p 9p 13p Check by multiplying. Factor Trinomials Using FOIL Example Look for a sum of +13p.
  • 5. Slide - 5Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor 28g2 + 39g + 5. Add. ( + 1 ) ( + 5 )28g g 140g 1g 141g Add. ( + 1 ) ( + 5 )g 28g 5g 28g 33g Add. ( + 1 ) ( + 5 )14g 2g 70g 2g 72g Add. ( + 1 ) ( + 5 )2g 14g 10g 14g 24g Factor Trinomials Using FOIL Example Look for a sum of +39g.
  • 6. Slide - 6Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor 28g2 + 39g + 5. Add. ( + 1 ) ( + 5 )7g 4g 35g 4g 39g Check by multiplying. Factor Trinomials Using FOIL Example (cont.) Look for a sum of +39g.
  • 7. Slide - 7Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example Factor 8n2 – 10n + 3. Add. ( – 1 ) ( – 3 )8n n –24n –1n –25n Add. ( – 1 ) ( – 3 )n 8n –3n –8n –11n Add. ( – 1 ) ( – 3 )4n 2n –12n –2n –14n Add. ( – 1 ) ( – 3 )2n 4n –6n –4n –10n Check by multiplying.Look for a sum of –10n.
  • 8. Slide - 8Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example Factor 10k2 – 19k + 7. Add. ( – 1 ) ( – 7 )10k k –70k –1k –71k Add. ( – 1 ) ( – 7 )k 10k –7k –10k –17k Add. ( – 1 ) ( – 7 )5k 2k –35k –2k –37k Add. ( – 1 ) ( – 7 )2k 5k –14k –5k –19k Check by multiplying.Look for a sum of –19k.
  • 9. Slide - 9Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example Factor 36d 2 + 4d – 7. Add. ( + 1 ) ( – 7 )36d d –252d 1d –251d Add. ( + 1 ) ( – 7 )d 36d – 7d 36d 29d Add. ( – 1 ) ( + 7 )36d d 252d –1d 251d Add. ( – 1 ) ( + 7 )d 36d 7d –36d –29d Look for a sum of +4d.
  • 10. Slide - 10Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example (cont.) Factor 36d 2 + 4d – 7. Add. ( + 1 ) ( – 7 )18d 2d –126d 2d –124d Add. ( + 1 ) ( – 7 )2d 18d – 14d 18d 4d Check by multiplying.Look for a sum of +4d.
  • 11. Slide - 11Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomial Using FOIL Example Factor 15a2 + 7a – 4. Add. ( + 1 ) ( – 4 )15a a –60a 1a –59a Add. ( + 1 ) ( – 4 )a 15a – 4a 15a 11a Add. ( – 1 ) ( + 4 )15a a 60a –1a 59a Add. ( – 1 ) ( + 4 )a 15a 4a –15a –11a Look for a sum of +7a.
  • 12. Slide - 12Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomial Using FOIL Example (cont.) Factor 15a2 + 7a – 4. Add. ( + 1 ) ( – 4 )5a 3a –20a 3a –17a Add. ( + 1 ) ( – 4 )3a 5a –12a 5a –7a Add. ( – 1 ) ( + 4 )5a 3a 20a –3a 17a Add. ( – 1 ) ( + 4 )3a 5a 12a –5a 7a Check by multiplying.Look for a sum of +7a.
  • 13. Slide - 13Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example Add. ( + 7y ) ( – 5y )3x 4x –15xy 28xy 13xy Look for a sum of –13xy.Factor 12x2 – 13xy – 35y2 Add. ( + 7y ) ( – 5y )4x 3x –20xy 21xy 1xy Add. ( – 7y ) ( + 5y )3x 4x 15xy –28xy –13xy Check by multiplying.
  • 14. Slide - 14Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Check by multiplying. Factor Trinomials Using FOIL Example Add. ( + 5b ) ( – 3b )8a 3a –24ab 15ab –9ab Look for a sum of +2ab.Factor 24a2 + 2ab – 15b2. Add. ( + 5b ) ( – 3b )3a 8a –9ab 40ab 31ab Add. ( + 5b ) ( – 3b )6a 4a –18ab 20ab 2ab
  • 15. Slide - 15Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example Add. ( + 5 ) ( + 2 )6y 3y 12y 15y 27y Check by multiplying.Look for a sum of +27y.Factor 90y3 + 135y2 + 50y. 90y3 + 135y2 + 50y = 5y (18y2 + 27y + 10) The completely factored form of 90y3 + 135y2 + 50y is 90y3 + 135y2 + 50y = 5y (6y + 5) (3y + 2)
  • 16. Slide - 16Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Factor Trinomials Using FOIL Example Add. ( – 3 ) ( – 2 )7x 2x –14x –6x –20x Check by multiplying.Look for a sum of –25x.Factor 42x3 – 75x2 + 18x. 42x3 – 75x2 + 18x = 3x (14x2 – 25x + 6) Add. ( – 3 ) ( – 2 )2x 7x –4x –21x –25x The completely factored form of 42x3 – 75x2 + 18x is 42x3 – 75x2 + 18x = 3x (2x – 3) (7x – 2)
  • 17. Slide - 17Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G Remember to include the common factor in the final factored form. CAUTION Factor Trinomials Using FOIL