Answer: x = -4 and x = 2.
To factor a quadratic equation in the form of x^2 + bx + c = 0, we need to find two numbers that when multiplied together, give us c, and when added or subtracted, give us b.
We need to find two numbers whose product is -8 and whose sum is 2. These numbers are 4 and -2, so we can write:
x^2 + 2x - 8 = (x + 4)(x - 2) = 0
Setting each factor to zero, we get:
x + 4 = 0 or x - 2 = 0
Solving for x in each equation, we get:
x = -4 or x = 2
So, the solutions to the equation x^2 + 2x - 8 = 0 are x = -4 and x = 2.