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

−12=x2−x
negative 12 equals x squared minus x

x2=2x+8

Answer 1

To determine which of the given quadratic equations can be solved by factoring, we need to rewrite each equation in the standard form \( ax^2 + bx + c = 0 \) and check if they can be factored easily.

1. **For \( x^2 = 4x - 10 \)**:
Rearranging gives us \( x^2 - 4x + 10 = 0 \).
This does not factor easily (the discriminant \( b^2 - 4ac = 16 - 40 < 0 \)).

2. **For \( x^2 + 9x = 8 \)**:
Rearranging gives us \( x^2 + 9x - 8 = 0 \).
This can be factored as \( (x + 8)(x + 1) = 0 \).

3. **For \( -12 = x^2 - x \)**:
Rearranging gives us \( x^2 - x + 12 = 0 \).
This does not factor easily either (the discriminant \( -47 < 0 \)).

4. **For \( x^2 = 2x + 8 \)**:
Rearranging gives us \( x^2 - 2x - 8 = 0 \).
This can also be factored as \( (x - 4)(x + 2) = 0 \).

From these analyses, the equations that can be solved by factoring are:

- \( x^2 + 9x = 8 \) (can be factored as \( (x + 8)(x + 1) = 0 \))
- \( x^2 = 2x + 8 \) (can be factored as \( (x - 4)(x + 2) = 0 \))

Thus, the ones that can be solved by factoring are:
- \( x^2 + 9x = 8 \)
- \( x^2 = 2x + 8 \)