Question

Solve for x by factoring x2+3x−10=0
. Select all that apply.(2 points)
Responses

x= -5
x= -5

x= -2
x= -2

x= -1
x= -1

x= 1
x= 1

x= 2
x= 2

x= 5

Answer 1

To solve the quadratic equation \(x^2 + 3x - 10 = 0\) by factoring, we first need to factor the quadratic expression.

We want to find two numbers that multiply to \(-10\) (the constant term) and add to \(3\) (the coefficient of the \(x\) term). The numbers that meet these criteria are \(5\) and \(-2\) because:

- \(5 \times (-2) = -10\)
- \(5 + (-2) = 3\)

Thus, we can factor the quadratic as follows:

\[
(x + 5)(x - 2) = 0
\]

Now, we can use the zero-product property. Set each factor equal to zero:

1. \(x + 5 = 0\) → \(x = -5\)
2. \(x - 2 = 0\) → \(x = 2\)

Therefore, the solutions to the equation \(x^2 + 3x - 10 = 0\) are:

- \(x = -5\)
- \(x = 2\)

Based on the response options you provided, the correct responses are:

- **x = -5**
- **x = 2**