Question

8. Solve for x by factoring x2+3x−10=0
. Select all that apply.(4 points)
Responses

x=−5
x is equal to negative 5

x=−2
x is equal to negative 2

x=−1
x is equal to negative 1

x=1
x is equal to 1

x=2
x is equal to 2

x=5

Answer 1

To solve the equation \( x^2 + 3x - 10 = 0 \) by factoring, we need to find two numbers that multiply to -10 (the constant term) and add up to 3 (the coefficient of the \( x \) term).

The factors of -10 that add up to 3 are 5 and -2. So, we can write:

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

Next, we can set each factor equal to zero:

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

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

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

Therefore, the correct responses are:

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

So the selections that apply are:
- x=−5
- x=2