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)

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

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

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

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

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

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

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

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 2 ) ( 6x 5 ) + + 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