Final answer:
The factored form of x² − x − 2 is (x − 2)(x + 1), which corresponds to Option 1. The numbers − 2 and 1 multiply to give − 2 and add to − 1, matching the coefficients of the original quadratic equation.
Step-by-step explanation:
To find the factored form of x² − x − 2, we need to identify two numbers that multiply to − 2 (the constant term) and add up to − 1 (the coefficient of the x term). The numbers that satisfy both conditions are − 2 and 1. Therefore, when factoring x² − x − 2, we get (x − 2)(x + 1) as the factored form, which corresponds to Option 1.
Generally, for a quadratic equation in the form ax² + bx + c = 0, we look for two numbers that multiply to ac (the product of the coefficient of x² and the constant term) and add up to b (the coefficient of x). The process of finding such numbers is an essential skill in algebra when working with quadratic equations and their solutions.
In this case, since the equation is x² − x − 2 = 0, the product ac is equal to − 2, and the sum b is − 1. The numbers matching these criteria are − 2 and 1, leading us to write the factored form as (x − 2)(x + 1).