Section 9-6Day 1

Factoring Trinomials

ax2 + bx + cDay 1

• Factoring using “ac” method:

If your first term is NEGATIVE, factor out the negative FIRST then continue!!

Example 16s2 – s – 5

Step 1: Multiply a * ca * c =

6 * 5 = 30

Step 2: Find factors of ac:30

1 30 2 15 3 10 5 6

Step 3: Find the set of factors that get “b” “c” term is NEGATIVE so we need to SUBTRACT to get b.

b = -1 ,What signs will make a -1?

– +

Example 1 cont.Step 4: REWRITE by breaking up the “bx” according to the pair: +5 and -6 6s2 + 5s – 6s – 5

Step 5: Factor by grouping: REMEMBER GCF Factoring!!

6s2 – s – 5

6s2 + 5s – 6s – 5

s (6s + 5)

NOTE: if this term is NEGATIVE, always take-out a NEGATIVE FACTOR

-1 (

6s + 5)

(s – 1)(6s + 5)

s s – 1 – 1

(6s + 5)

(6s + 5)

Example 2 –6k2 – 13k – 6

Step 1: Multiply a * c

a * c =

6 * 6 = 36 Step 2: Find all factors of ac:

36 1 36 2 18 3 12 4 9

Step 3: Find the set of factors that get “b” “c” term is POSITIVE so we need to ADD to get b.

If your first term is NEGATIVE, factor out the negative FIRST, then continue

REWRITE:-1 (

6k2 + 13k + 6)

6 6

b = +13,What signs will make a +13?

+ +

Example 1 cont.Step 4: REWRITE by breaking up the “bx” according to the pair: +4 and +9 6k2 + 4k + 9k + 6

Step 5: Factor by grouping: REMEMBER GCF Factoring!!

6k2 + 13k + 6

6k2 + 4k + 9k + 6

2k (3k + 2)

3 (3k + 2)

(2k + 3)

(3k + 2)

Don’t forget the -1 out front!

-1

2k 2k 3 3

(3k + 2)

(3k + 2)

Homework:

Pg 5964 – 9,

11 – 14, 16 – 21