Question

Which of the following quadratic equations can be solved by factoring?(1 point)
Responses

x2=4x−10
x squared equals 4 x minus 10

x2+9x=8
x squared plus 9 x equals 8

x2=2x+8
x squared equals 2 x plus 8

−12=x2−x

Answer 1

To determine which of the given quadratic equations can be solved by factoring, we will rearrange them into the standard form \( ax^2 + bx + c = 0 \) and check if they can be factored easily.

1. **\( x^2 = 4x - 10 \)**
Rearranging gives:
\( x^2 - 4x + 10 = 0 \)
This cannot be factored easily into rational numbers.

2. **\( x^2 + 9x = 8 \)**
Rearranging gives:
\( x^2 + 9x - 8 = 0 \)
Check if it factors:
The factors of \(-8\) that add to \(9\) are \(10\) and \(-1\), so it can be factored as:
\( (x + 10)(x - 1) = 0 \)

3. **\( x^2 = 2x + 8 \)**
Rearranging gives:
\( x^2 - 2x - 8 = 0 \)
Check if it factors:
The factors of \(-8\) that add to \(-2\) are \(-4\) and \(2\), so it can be factored as:
\( (x - 4)(x + 2) = 0 \)

4. **\( -12 = x^2 - x \)**
Rearranging gives:
\( x^2 - x + 12 = 0 \)
This cannot be factored easily into rational numbers (the discriminant is negative).

Based on the analysis, the equations that can be solved by factoring are:

- \( x^2 + 9x = 8 \)
- \( x^2 = 2x + 8 \)

Therefore, the **correct responses are**:
- **\( x^2 + 9x = 8 \)**
- **\( x^2 = 2x + 8 \)**