1. Factoring Quadratic Equations when a = 1

2. FACTORING FACTS
This sign comes from multiplying the last terms together when multiplying the polynomials together.
If +, then both factors have to be the same. Either + + or - -
If -, then signs are different + -
This sign also tells us if we are adding or subtracting factors to get the middle term (bx).
If +, you are adding.
If -, you are subtracting.

3. # 1
x2 + 7x + 12
Since C is +, both signs have to be the same
+ & + or - & -. Since b is positive, they are both +
Step 1: Fill in x. 12
Step 2: Signs ac + 3 + 4
Step 4: Write the factors b
(x+3)(x+4) 7
Step 3: Factors of a•c
Since C is +, we are looking for the factors that add to give us 7.
1•12 = 1 • 12
= 2 • 6
= 3 • 4

4. # 2 12 ac - 2 - 6 b (x-2)(x-6) -8 Factor. x2 - 8x +12
Since C is +, both signs have to be the same
+ & + or - & -. Since b is negative, they are both -
Step 1: Fill in x. 12
Step 2: Signs ac - 2 - 6
Step 4: Write the factors b
(x-2)(x-6) -8
Step 3: Factors of a•c
Since C is +, we are looking for the factors that add to give us 8.
1•12 = 1 • 12
= 2 • 6
= 3 • 4

5. # 3 -24 ac - 4 + 6 b (x-4)(x+6) 2 Factor. x2 + 2x - 24
Since C is -, one has to be – and one is +.
Step 1: Fill in x.
-24
Step 2: Signs ac - 4 + 6
Step 4: Write the factors b
(x-4)(x+6)
Sign of
Larger
number 2
Step 3: Factors of a•c
1•24 = 1 • 24
= 2 • 12
= 3 • 8
= 4 • 6
So is it:
4 and -6 or -4 and 6 to give you +2
Since C is -, we are looking for the factors that subtract to give us 2.

6. # 4 -24 ac - 12 + 2 b (x-12)(x+2) -10 Factor. x2 - 10x - 24
Since C is -, one has to be – and one is +.
Step 1: Fill in x.
-24
Step 2: Signs ac - 12 + 2
Step 4: Write the factors b
(x-12)(x+2)
-10
Sign of
Larger
number
Step 3: Factors of a•c
1•24 = 1 • 24
= 2 • 12
= 3 • 8
= 4 • 6
So is it:
2 and -12 or -2 and 12 to give you -10
Since C is -, we are looking for the factors that subtract to give us 10.

7. Practice Problems (t – 7)(t + 3) (x +8)(x +4) (x-6)(x – 4)
Factor each trinomial, if possible.
1) t2 – 4t – 21
2) x2 + 12x + 32
3) x2 –10x + 24
4) x2 + 3x – 18
(t – 7)(t + 3)
(x +8)(x +4)
(x-6)(x – 4)
(x +6)(x – 3)