1. FACTORING TRINOMIALS with leading coefficient
ax2 + bx + c to
(ax + b)(cx + d)

2. Now we need to factor trinomials with other leading coefficients!
For example:
THE FIRST STEP IS TO ALWAYS CHECK IF YOU CAN FACTOR OUT A GCF
Example 1:
Example 2:
2x2 – 4x – What is the GCF?
2(x2 – 2x – 35) Factor as normal!
So 2x2 – 4x – 70 = 2(x + 5)(x – 7).
3x2 – 33x What is the GCF?
3(x2 – 11x +24) Factor as normal!
So 3x2 – 33x + 72 = 3(x - 3)(x – 8).

3. First check to see if there is a GCF we can factor out… is there?
Step 1: Multiply the first and last terms’ coefficients.
(21)(-4) =-84
Step 2: Find factors of -84 that add to -5
-84 means one factor is + one factor is -
Step 3: Replace the middle term with these factors.
Step 4: Factor by grouping.
First check to see if there is a GCF we can factor out… is there?
No, so we expand it to make 4 terms then factor by grouping!
Factors of -84
(larger is - )
Difference of
factors = -5

4. First check to see if there is a GCF we can factor out… is there?
Step 1: Multiply the first and last terms’ coefficients.
(25)(9) =225
Step 2: Find factors of 225 that add to -30
225 means both factors are + or both are -
Step 3: Replace the middle term with these factors.
Step 4: Factor by grouping.
First check to see if there is a GCF we can factor out… is there?
No, so we expand it to make 4 terms then factor by grouping!
Sum of
factors = -30
Factors of 225

5. First check to see if there is a GCF we can factor out… is there?
Step 1: Multiply the first and last terms’ coefficients.
(2)(9) =18
Step 2: Find factors of 18 that add to -9
18 means one factor is + one factor is -
Step 3: Replace the middle term with these factors.
Step 4: Factor by grouping.
First check to see if there is a GCF we can factor out… is there?
No, so we expand it to make 4 terms then factor by grouping!
Factors of 18
(both are - )
Sum of
factors = -9

6. First check to see if there is a GCF we can factor out… is there?
Step 1: Multiply the first and last terms’ coefficients.
(12)(5) =60
Step 2: Find factors of 60 that add to 19
60 means both factors are + or both are -
Step 3: Replace the middle term with these factors.
Step 4: Factor by grouping.
First check to see if there is a GCF we can factor out… is there?
No, so we expand it to make 4 terms then factor by grouping!
Factors of 60
(both are + )
Sum of
factors = 19

7. Put in descending order first!!
What's different here?
It's out of order...
Put in descending order first!!
Now follow
the same steps!
Sum of
factors = +33
Factors of 200
(both are + )

8. Put in descending order first!!
What's different here?
It's out of order...
Put in descending order first!!
Now follow
the same steps!
Sum of
factors = +3
Factors of -40
(larger is + )

9. Using grouping with trinomials
Multiply the first and last coefficients.
4(7) = 28
Find the factors of 28 that add to -1
None of the factors will ADD to give -1
Using grouping with trinomials
DOES NOT FACTOR!!!
Sum of
factors = -1
Factors of 28
(both are - )

10. Using grouping with trinomials
Multiply the first and last terms.
3(-5) = -15
Find the factors of -15 that add to 7
None of the factors will SUBTRACT to give +7
Using grouping with trinomials
DOES NOT FACTOR!!!
Factors of -15
(larger is + )
Sum of
factors = +7