6 3 Factoring Trinomials of the Form ax

6. 3 Factoring Trinomials of the Form ax 2 + bx + c, where a 1 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.

Factoring Trinomials of the Form ax 2 + bx + c What still works? t. ns en er ff e ar di g Si e. n Sig re sa th am es

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

Factor by Grouping: osi p th Bo . tive e. m D. sa D e th t. A a e h r t a ns ors t g i c a S F 30 + + Check by foiling!

Factor by Grouping: tor c a rf e e g Lar egativ is n T. C A nt. TR e B r e U iff d t. S a e h r t a ns ors t g i c S Fa 60 + - Check by foiling!

Factor by Grouping: 24 - + Check by foiling!

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

Multip ly Illegal Method: . ∙ 4 ILLEGAL ÷ 4 Check by foiling!

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

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

Guess & Check: ferent. if Signs are d 3∙ 5 1∙ 15 2∙ 2 1∙ 4 3 2 4 1 – 5 2 1 4 + –

Guess & Check: 1∙ 3 2∙ 4 1∙ 8

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

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

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

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