To determine which of the given quadratic equations can be solved by factoring, we need to rearrange each equation into standard form (ax² + bx + c = 0) and check if they can be factored.
-
x² + 9x = 8
Rearranging gives:
x² + 9x - 8 = 0
This can potentially be factored. -
x² = 2x + 8
Rearranging gives:
x² - 2x - 8 = 0
This can potentially be factored. -
−12 = x² − x
Rearranging gives:
x² - x + 12 = 0
This does not factor easily (the discriminant is negative). -
x² = 4x − 10
Rearranging gives:
x² - 4x + 10 = 0
This does not factor easily (the discriminant is negative).
Based on this analysis, the quadratic equations that can be solved by factoring are:
- x² + 9x = 8
- x² = 2x + 8
So, the response includes the first and second equations.