Factoring: Example 2

Factoring

Factor and solve x² - 2x - 8 = 0.

Step 1. List all factor pairs of c.

In this equation c = -8.
The factor pairs of -8 are 1 and -8, -1 and 8, -2 and 4, 2 and -4.

Step 2. Determine which factor pair has a sum of b.

In this equation b = -2.
The sum of the factor pairs are -8 + 1 = -7, -1 + 8 = 7, -2 + 4 = 2, and 2 + -4 = -2.

2 and -4 have the correct sum.

Step 3. Substitute the roots into the factored form.

(x + 2)(x - 4) = 0

Step 4. Use the Zero Product Property to set each factor equal to zero and solve.

x + 2 = 0 or x - 4 = 0

x = -2 or x = 4