1. Factoring Algebraic Expressions Complex Trinomials
Factor the following:
We need to consider different arrangements of the factors of the first and last terms
6x2 + 7x – 10
Factors of 6
Factors of 10
Write the factors in organized columns 1 6 2 3 1 10 2 5 5 2 10 1
You only need the “reverse” factors on one side
You need to find pairs of products that subtract…
Look at the cross-products of the factors
to give the middle term (7)

2. Factoring Algebraic Expressions Complex Trinomials
6x2 + 7x – 10
You need to find pairs of products that subtract to give the middle term
Factors of 6
Factors of 10 1 6 2 3 1 10 2 5 5 2 10 1
Don’t worry about the sign on the difference… yet 3 20
Subtract to give 17
But the middle term is 7, so we have to try the next pair

3. Factoring Algebraic Expressions Complex Trinomials
6x2 + 7x – 10
You need to find pairs of products that subtract to give the middle term
Factors of 6
Factors of 10 1 6 2 3 1 10 2 5 5 2 10 1 6 10
Subtract to give 4… no good

4. Factoring Algebraic Expressions Complex Trinomials
6x2 + 7x – 10
You need to find pairs of products that subtract to give the middle term
Factors of 6
Factors of 10 1 6 2 3 1 10 2 5 5 2 10 1 15 4
Subtract to give 11… no good

5. Factoring Algebraic Expressions Complex Trinomials
6x2 + 7x – 10
You need to find pairs of products that subtract to give the middle term
Factors of 6
Factors of 10 1 6 2 3 1 10 2 5 5 2 10 1 30 2
Subtract to give 28… no good 2 3
We’ve tried all of the products with 1 6
So now we try products with

6. Factoring Algebraic Expressions Complex Trinomials
6x2 + 7x – 10
You need to find pairs of products that subtract to give the middle term
Factors of 6
Factors of 10 1 6 2 3 1 10 2 5 5 2 10 1 6 10
Subtract to give 4… no good 2 3
We’ve tried all of the products with 1 6
So now we try products with

7. Factoring Algebraic Expressions Complex Trinomials
6x2 + 7x – 10
You need to find pairs of products that subtract to give the middle term
Factors of 6
Factors of 10 1 6 2 3 1 10 2 5 5 2 10 1
Circle the pairs that work. We need these to form the binomial factors 12 5
Subtract to give 7… that’s what we need!
We have the middle term, so that means these are the pairs of factors we need

8. Factoring Algebraic Expressions Complex Trinomials
6x2 + 7x – 10
You need to find pairs of products that subtract to give the middle term
Factors of 6
Factors of 10 1 2 1 6 2 3 1 10 2 5 5 2 10 1
Circle the pairs that work. We need these to form the binomial factors 6 5
Now dress it up with the variables 12 5
Subtract to give 7… that’s what we need!
( ) ( ) x x
We have the middle term, so that means these are the pairs of factors we need
To determine the signs, you need, look at the original trinomial

9. Factoring Algebraic Expressions Complex Trinomials
To determine the signs, you need to look at the original trinomial
6x2 + 7x – 10
Factors of 6
Factors of 10
The – sign on the last term means that the signs are different 1 6 2 3 1 10 2 5 5 2 10 1
The + sign on the middle term means that the sign on the bigger product is +
(1x ) ( 6x ) + +
Check the “OI” of FOIL. In this case, the bigger product is 12x
12x – – 5x
12x must be positive
5x must be negative
Remember to check your answer by doing FOIL