1. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.3 – Slide 1

2. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.3 – Slide 2 Factoring and Applications Chapter 6

3. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.3 – Slide 3 6.3 Factoring Trinomials by Grouping

4. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.3 – Slide 4 6.3 Factoring Trinomials by Grouping Objectives 1.Factor trinomials by grouping when the coefficient of the squared term is not 1.

5. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.3 – Slide 5 6.3 Factoring Trinomials by Grouping Factoring Trinomials by Grouping Factor the trinomial 3x + 14x + 8. 2 Sum is 14. Product is 24. 124 212 38 46 Find a product of 24 and a sum of 14. 3x + x + x + 8 2 3x + 14x + 8 2 212 x ( 3x + 2 )+ 4 ( 3x + 2 ) ( 3x + 2 )( x + 4 ) ( 3x + 2 )( x + 4 ) =Check:3x + 14x + 8 2 Example 1

6. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.3 – Slide 6 6.3 Factoring Trinomials by Grouping Factoring Trinomials by Grouping Factor the trinomial 10n + 3n – 1. 2 10n + 3n – 1 2 Sum is 3. Product is – 10. 1 – 10 2 –5–5 Find a product of –10 and a sum of 3. 10n + n – n – 1 2 52 5n ( 2n + 1 )– 1 ( 2n + 1 ) ( 2n + 1 )( 5n – 1 ) ( 2n + 1 )( 5n – 1 ) =Check:10n + 3n – 1 2 –1–1 10 –2–2 5 Example 2

7. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.3 – Slide 7 6.3 Factoring Trinomials by Grouping Factoring Trinomials by Grouping Factor the trinomial 2y + 5y – 12. 2 2y + 5y – 12 2 Sum is 5. Product is – 24. –1–1 24 –2–2 12 –3–3 8 –4–4 6 Find a product of –24 and a sum of 5. 2y + y – y – 12 2 83 2y ( y + 4 )– 3 ( y + 4 ) ( y + 4 )( 2y – 3 ) ( y + 4 )( 2y – 3 ) =Check:2y + 5y – 12 2 Example 3

8. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.3 – Slide 8 6.3 Factoring Trinomials by Grouping Factoring Trinomials by Grouping Factor the trinomial 20g – g – 1. 2 Sum is – 1. Product is – 20. 1 – 20 2 – 10 4 –5–5 Find a product of –20 and a sum of –1. 20g + g – g – 1 2 45 4g ( 5g + 1 ) – 1 ( 5g + 1 ) ( 5g + 1 )( 4g – 1 ) 20g – g – 1 2 Check:( 5g + 1 )( 4g – 1 ) =20g – g – 1 2 Example 4

9. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.3 – Slide 9 6.3 Factoring Trinomials by Grouping Factoring Trinomials by Grouping –1–1 36 –2–2 18 –3–3 12 Find a product of – 36 and a sum of 5. Factor 12x + 10x – 12x. 543 12x + 10x – 12x 543 2x ( 6x + 5x – 6 ) 32 = 3 2x2x= 2 ( 6x + x – x – 6 ) –4–4 9 –6–6 6 94 3 2x2x= ( 3x ( 2x + 3 )– 2 ( 2x + 3 ) ) 3 2x2x= ( ( 2x + 3 )( 3x – 2 ) ) 3 2x2x=( 2x + 3 )( 3x – 2 ) Example 5

10. Copyright © 2010 Pearson Education, Inc. All rights reserved. 6.3 – Slide 10 6.3 Factoring Trinomials by Grouping Factoring Trinomials by Grouping Factor 12x + 10x – 12x. 543 Check: 3 2x2x( 2x + 3 ) ( 3x – 2 ) 4 ( 4x ( 3x – 2 ) + 6x ) 3 5 12x– 8x 4 = = + 18x 4 – 12x 3 = 12x + 10x – 12x 543 Example 5 (continued)