How do you factor this equation?
x^2+x-2=0
As simple as (x+2)(x-1) = 0
I don't understand how you do this.
To factor the quadratic equation x^2 + x - 2 = 0, we need to find two binomial expressions whose factors multiply to give the trinomial. Here's a step-by-step process to factor the equation:
Step 1: Ensure that the quadratic equation is in standard form, where the highest power of x has a coefficient of 1. In this case, the equation is already in standard form.
Step 2: Identify the values of a, b, and c in the quadratic equation ax^2 + bx + c = 0. In our equation, a = 1, b = 1, and c = -2.
Step 3: Find two numbers whose product is equal to ac (a * c) and whose sum is equal to b. In our equation, ac is equal to 1 * -2 = -2, and b is equal to 1. So, we need to find two numbers that multiply to -2 and add up to 1.
Step 4: The two numbers that satisfy the conditions above are 2 and -1. 2 * -1 = -2, and 2 + (-1) = 1.
Step 5: Rewrite the middle term of the quadratic equation using the two numbers found in Step 4, and group the terms:
x^2 + 2x - x - 2 = 0
Step 6: Factor by grouping. Factor out the greatest common factor from the first two terms and the last two terms:
x(x + 2) - 1(x + 2) = 0
Step 7: Observe that we now have a common binomial factor of (x + 2):
(x - 1)(x + 2) = 0
Step 8: Apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero:
x - 1 = 0 or x + 2 = 0
Step 9: Solve for x in each equation:
For x - 1 = 0:
x = 1
For x + 2 = 0:
x = -2
So the solutions to the quadratic equation x^2 + x - 2 = 0 are x = 1 and x = -2.