Day Problems • Factor each expression. Check your answer.

1. r 2 + 4r + 3 2. x 2 – 2x + 1 3. m 2 + 3m – 10 4. a 2 + 19a + 18 5. w 2 – 13w – 30

9.6 Factoring Trinomials of the Type ax 2 + bx + c • When c is positive Multiply a and c together.

Find the factors of that number.

What factors add together to give you b?

C is Positive • Factor 6n 2 6 + 23n + 7.

n

2  23

n

 7 6(7)  42

• Factor 6n 2 + 23n + 7.

6

n

2 6

n

2  23

n

 7  2

n

 21

n

 7 (2

n

 1)  7(3

n

 1)  7)(3

n

 1)

C is Negative • Factor 7x 2 7 – 26x – 8.

x

2  26

x

 8 56 2   28 4   14 26 10

C is Negative • Factor 7x 2 7 – 26x – 8.

x

2  26

x

 8 7

x

2  28

x

 2

x

 8 (7

x

  4) 2)(  2(

x x

  4) 4)

Factoring Out a Monomial First • Factor 20x 2 + 80x +35 completely.

2 20 5(4

x x

7(4)  80 2   16 28

x x

  35 7)

5(4

x

2  16

x

 7) 5(4

x

2  2

x

 14

x

 7)

x

 1)  7(2

x

 1) 5(2

x

 1)(2

x

 7)