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

Question

Responses

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

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

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

x2=4x−10

Answer 1

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

1. −12 = x² - x
   Rearranging gives:
   \( x² - x + 12 = 0 \)
   This does not factor easily (no integer factors of 12 that add to -1).

2. x² = 2x + 8
   Rearranging gives:
   \( x² - 2x - 8 = 0 \)
   This can be factored as \( (x - 4)(x + 2) = 0 \).

3. x² + 9x = 8
   Rearranging gives:
   \( x² + 9x - 8 = 0 \)
   This also does not factor easily (no integer factors of -8 that add to 9).

4. x² = 4x - 10
   Rearranging gives:
   \( x² - 4x + 10 = 0 \)
   This does not factor easily (discriminant is negative).

Based on this analysis, the quadratic equation that can be solved by factoring is:

x² = 2x + 8 (which can be rearranged to \( x² - 2x - 8 = 0 \) and factored).