Download 1. Multiply ac

Factoring Quadratic
Trinomials
2
ax +bx+c
Remember:
Factored Form Foil
Trinomial Form
2
2
(x+3)(x+2)
x +2x+3x+6 x + 5x + 6
2
2
(x-2)(x+3)
x +3x-2x-6
x +x - 6
To factor trinomials, look at
the a,b,c numbers
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 )
2
x -x-12
1. Multiply ac
2. Set up
t-chart
(x+3)(x-4)
1(-12)=-12
ac=-12
Sum=-1
b
one + one 1(-12)
-11
-1(12)
11
-2(6)
4
2(-6)
-4
3(-4)
-1
Factor
2
x -
1. Multiply ac
2. Set up
t-chart
(x - 2)(x - 3)
5x + 6
1(6)=6
ac=6
Sum=-5
two -
b
-1(-6)
-7
-2(-3)
-5
Factor when 1 isn’t the
number in front of x2
6x2 + 7x-5
1. Multiply ac 6(-5)=-30
2. Set up
ac=-30
t-chart
one + one 3. Since you have a
coefficient greater than 1,
take your factored terms
and factor them too.
(2x - 1)(3x + 5)
-1(30)
1(-30)
-2(15)
2(-15)
-3(10)
Sum=7
b
29
-29
13
-13
7
What happens when you can’t find
factors?????
Use the discriminate to
show a trinomial won’t factor
2
-2x +3x-6
32 - 4(-2)(-6)
9 – 48
-39
No Real Solutions!