Factoring Trinomials
The A-C Method
Ax2 + Bx + C
Step 1: Factor out any GCF that
may exist.
X2 – 7X + 10
Step 2: Multiply the A and C coefficients
and put the product in the right hand
corner.
X2 – 7X + 10
Step 2: Multiply you’re A and C
coefficients and put the product in the
right hand corner.
X2
– 7X + 10
10
Step 3: Bring down the first and third
terms and draw a line down the middle.
– 7X + 10
X2
|
10
|
|
X2
10
Step 4: Look at the second operation, Is
it addition or subtraction?
X2
X2
10
– 7X + 10
|
10
|
|
• If the second operation is addition:
Choose two factors of the AC product which add to make the
middle term.
• If the second operation is subtraction:
Choose two factors of the AC product which subtract to make the
middle term.
Step 5: Place one factor on each side of
the line along with the middle term’s
variable.
X2
X2
10
– 7X + 10
5X | 2X 10
|
|
• Since the second operation is addition, I am choosing 5
and 2.
Step 6: Factor out the Greatest Common
Factor from each side.
10
– 7X + 10
X2
5X | 2X 10
X (X 5) | 2 (X 5)
|
X2
Step 7: Factor out the common factor.
10
– 7X + 10
X2
5X | 2X 10
X (X 5) | 2 (X 5)
|
(X 5) | (X 2)
X2
Step 8: Determine the signs.
10
– 7X + 10
X2
5X | 2X 10
X (X 5) | 2 (X 5)
|
(X - 5) | (X - 2)
X2
Now try these examples.
+ 3X – 28
3X2 – 11X – 4
6X2 + X - 15
2
Example 2 X
Example 3
Example 4
Your Homework Assignment is:
PAGE
Step 1: Factor out any GCF that
may exist.
6X2 + X -15
Step 2: Multiply the A and C coefficients
and put the product in the right hand
corner.
6X2 + X -15
Step 2: Multiply you’re A and C
coefficients and put the product in the
right hand corner.
6X2
+ X -15
90
Step 3: Bring down the first and third
terms and draw a line down the middle.
6X2
6X2
90
+ X -15
|
15
|
|
Step 4: Look at the second operation, Is
it addition or subtraction?
6X2
6X2
90
+ X -15
|
15
|
|
• If the second operation is addition:
Choose two factors of the AC product which add to make the
middle term.
• If the second operation is subtraction:
Choose two factors of the AC product which subtract to make the
middle term.
Step 5: Place one factor on each side of
the line along with the middle term’s
variable.
6X2
6X2
90
+ X -15
9X | 10X 15
|
|
• Since the second operation is subtraction, I am choosing 9
and 10.
Step 6: Factor out the Greatest Common
Factor from each side.
6X2
90
+ X -15
6X2 9X | 10X 15
3X(2X 3)| 5(2X 3)
|
Step 7: Factor out the common factor.
6X2
90
+ X -15
6X2 9X | 10X 15
3X (2X 3)| 5(2X 3)
(2X 3)| (3X 5)
Step 8: Determine the signs.
2
6X
90
+ X -15
2
6X
9X | 10X 15
3X (2X 3)| 5(2X 3)
(2X - 3) (3X + 5)