Question

solve using factoring.
$x^2 + x - 2 = 0$
select the correct response:
2, 1
-2, -1
2, -1
-2, 1

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to $-2$ (the constant term) and add up to $1$ (the coefficient of $x$). The numbers are $2$ and $-1$ because $2\times(-1)= -2$ and $2 + (-1)=1$. So we can factor the quadratic as:
$$x^{2}+x - 2=(x + 2)(x - 1)=0$$

Step2: Solve for $x$

Set each factor equal to zero:

• For $x + 2 = 0$, we get $x=-2$.
• For $x - 1 = 0$, we get $x = 1$.

Answer:

-2, 1 (corresponding to the option: -2, 1)