1. Factoring Quadratic Trinomials
10.5
Factoring Quadratic Trinomials

2. To factor trinomials, look at the a,b,c numbers
ax2+bx+c
Remember:
To factor trinomials, look at the a,b,c numbers

3. 3. Look for factors of “ac” that added together give you “b”
Steps to Follow:
1. Multiply a*c
2. Set up a t-chart
3. Look for factors of “ac” that added together give you “b”
4. Write answer in (x )(x )

4. x2-x-12 1(-12)=-12 1. Multiply ac 2. Set up t-chart (x+3)(x-4) ac=-12
one + one -
Sum=-1 b
1(-12)
-11 11
-1(12)
-2(6) 4
(x+3)(x-4)
2(-6) -4 -1
3(-4)

5. Factor x2- 5x + 6 1(6)=6 (x - 2)(x - 3) 1. Multiply ac
2. Set up t-chart
ac=6
two -
Sum=-5 b
-1(-6) -7 -5
-2(-3)
(x - 2)(x - 3)

6. Factor when 1 isn’t the number in front of x2
6x2 + 7x-5
1. Multiply ac
6(-5)=-30
2. Set up t-chart
3. Since you have a coefficient greater than 1, take your factored terms and factor them too.
ac=-30
one + one -
Sum=7 b
-1(30) 29
1(-30) -2(15) 2(-15) -3(10)
(2x - 1)(3x + 5)

7. Use the discriminate to show a trinomial won’t factor
What happens when you can’t find factors?????
Use the discriminate to show a trinomial won’t factor
-2x2+3x-6
32 - 4(-2)(-6)
9 – 48
-39
No Real Solutions!