Factoring a tri-nominal that has a coefficient greater than 1

Follow these steps. (Use this form, ax² + bx + c)

example 3x² + 5x + 2


1. multiply the first (a) and last coefficient (c)-------- 3 times 2 = 6

2. Now, find two factors of 6 that add up to the middle coefficient, (b), in this example its 5. Hmmmm, two numbers that make a product of 6 and a sum of 5, let’s see…….. I know, 2 and 3. CORRECT! 2 x 3 = 6 and 2+ 3 = 5

3. Split the middle term (5x) up with the new factors (2 and 3).

Re-write it now: it should look like this 3x² + 2x + 3x +2 order of 2 and 3 does not matter.

4. Next break in 2 groups, like this. (3x² +2x) (3x + 2) * Tricky part* find the GCF of both bi-nominal x is the GCF for the first and 1 is the GCF for the 2nd.

5. Divide each bi-nominal by its GCF.

It looks like this: (3x² + 2x) + (3x + 2)
X( 3x +2) 1(3x + 2) ( I divided each bi-nominal by its own gcf.)

6. Finally, get a GCF for the entire problem. X(3x +2) 1(3x +2) the GCF is 3x + 2
DIVIDE by 3x + 2

Answer (3x +2) (x + 1)

NOW CHECK USING F O I L
Combine 2x and 3x to get 5x
F= 3x times x = 3x²
O = 3x times 1 = 3x ---- Combine the like terms to get 5x
I = 2 times x = 2x
L = 2 times 1 = 2

Now put it together and get the original tri-nominal.

3x² +5x + 2 Eureka you did it!