1. Factoring Trinomials of the Form ax 2 + bx + c, where a  1 6.3 1.Factor trinomials of the form ax 2 + bx + c, where a  1, by trial. 2.Factor trinomials of the form ax 2 + bx + c, where a  1, by grouping.

2. Factoring Trinomials of the Form ax 2 + bx + c What still works? Signs are the same. Signs are different.

3. Factoring Trinomials of the Form ax 2 + bx + c Factors of 24 that subtract to equal 10 24 Sign of the larger factor. Factors of 30 that subtract to equal 13 30 Sign of the larger factor. Factors of 60 that add to equal 23 60 Both signs are positive. 1 ∙ 24 2 ∙ 12 3 ∙ 8 4 ∙ 6

4. Factor by Grouping: 30 + + Signs are the same. Factors that ADD. Both positive. Check by foiling!

5. Factor by Grouping: 60 + - Signs are different. Factors that SUBTRACT. Larger factor is negative Check by foiling!

6. Factor by Grouping: 24 + - Check by foiling!

7. Illegal Method: ∙ 3 ILLEGAL ILLEGAL ÷ 3 Check by foiling! Multiply.

8. Illegal Method: ∙ 4 ILLEGAL ÷ 4 Check by foiling! Multiply. ILLEGAL

9. Illegal Method: ∙ 3 ILLEGAL ILLEGAL ÷ 3 Check by foiling!

10. Guess & Check: 1∙3 2∙5 1∙10 1 10 1 2 5

11. Guess & Check: 2∙2 1∙4 3∙5 1∙15 2 2 3 5 1 4 3 5 4 1 3 5 Signs are different. – + –

12. Guess & Check: 1∙3 2∙4 1∙8

13. Slide 6- 13 Copyright © 2011 Pearson Education, Inc. Factor completely. 2x 2 +3x – 20 a) (2x + 2)(x – 10) b) (2x + 4)(x – 5) c) (2x – 5)(x + 4) d) (2x – 10)(x + 2) 6.3

14. Slide 6- 14 Copyright © 2011 Pearson Education, Inc. Factor completely. 2x 2 +3x – 20 a) (2x + 2)(x – 10) b) (2x + 4)(x – 5) c) (2x – 5)(x + 4) d) (2x – 10)(x + 2) 6.3

15. Slide 6- 15 Copyright © 2011 Pearson Education, Inc. Factor completely. 6x 2 –33x – 63 a) 3(2x + 7)(x – 3) b) 3(2x + 3)(x – 7) c) 3(2x – 3)(x + 7) d) 3(2x – 7)(x + 3) 6.3

16. Slide 6- 16 Copyright © 2011 Pearson Education, Inc. Factor completely. 6x 2 –33x – 63 a) 3(2x + 7)(x – 3) b) 3(2x + 3)(x – 7) c) 3(2x – 3)(x + 7) d) 3(2x – 7)(x + 3) 6.3