Several Methods

1. Trial and Error – More mental math

2. Grouping – Longer method

FACTORING TRINOMIALS WITH LEADING COEFFICIENT > 1

TRIAL AND ERRORExample #1 (FROM HANDOUT)3p2 – 2p – 5

• First find any GCF

• List factors of 1st and last term

Factors of 3 Factors of 5

• (3, 1) (5, 1)

• Try factors in binomial form; (3x -5)(x + 1)

TRIAL AND ERROR

Ex; 3x2 + 17x + 10

Factor out any GCF

List factors of 1st and last terms

Factors of 3 Factors of 10

(3, 1) (2, 5) (1, 10)

Try combinations in binomial form;

Solution; (3x + 2)(x + 5)

GROUPING EXAMPLE; 3X2 + 17X + 10

Step 1; Check for GCF

Step 2: Multiply 1st and last term; 30

Step 3: List all factors; (1, 30), (2, 15), (3, 10), (5, 6)

Step 4: Select factors whose sum equal middle term (2, 15)

Step 5: Split middle term into new found factors

3x2 + 2x + 15x +10

Step 6: Use Grouping to complete factorization

x(3x + 2) + 5(3x + 2)

Solution: (3x + 2)(x + 5)

GROUPINGEXAMPLE #2 (FROM HANDOUT)

2n2 + 3n – 9

Check GCF

Multiply 1st and last term; -18

Factors of last term; (1, -18), (-1, 18), (2, -9), (-2, 9), (-3, 6), (3, -6)

Select factors whose sum equals middle term; (-3, 6)

Split middle term into new found factors;

2n2 – 3n + 6n – 9

Group and factor completely

n(2n – 3) + 3(2n – 3)

Solution; (2n – 3)(n + 3)