x^2+2x-8=0 solve by factoring and explain

Answer 1

To solve the equation x^2 + 2x - 8 = 0 by factoring, we need to find two numbers that multiply to -8 and add up to 2.

The factors of -8 are -1, 1, -2, 2, -4, and 4. Among these, the pair that adds up to 2 is 4 and -2.

Therefore, we can rewrite the equation as:

x^2 + 4x - 2x - 8 = 0
x(x + 4) - 2(x + 4) = 0
(x - 2)(x + 4) = 0

Now we can set each factor to zero and solve for x:

x - 2 = 0
x = 2

x + 4 = 0
x = -4

Therefore, the solutions to the equation x^2 + 2x - 8 = 0 are x = 2 and x = -4.