Factoring
Factoring
Example 1
Factor and solve x2 + 7x + 6 = 0
Step 1. List all factor pairs of c.
In this equation c = 6. The factor pairs of 6 are 1 and 6, 2 and 3.
Step 2. Determine which factor pair has a sum of b.
In this equation b = 7.
The sum of the factor pairs are 1 + 6 = 7 and 2 + 3 = 5.
1 and 6 have the correct sum.
Step 3. Substitute the roots into the factored form.
(x + 1)(x + 6) = 0
Step 4. Use the Zero Product Property to set each factor equal to zero and solve.
x + 1 = 0 or x + 6 = 0
x = -1 or x = -6
*Note: The Commutative Property of Multiplication says that order does not matter in multiplication, so the factored form could also be written ( x + 6)( x + 1).