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

Question

Responses

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

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

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

x2=2x+8

Answer 1

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

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

2. \( -12 = x^2 - x \)
   Rearranging gives:
   \( x^2 - x + 12 = 0 \)
   This cannot be factored easily (the factors of 12 do not give a difference of 1).

3. \( x^2 = 4x - 10 \)
   Rearranging gives:
   \( x^2 - 4x + 10 = 0 \)
   This cannot be factored easily (the discriminant is negative).

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

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

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

If you need to choose just one, focusing on the one with simpler, integer factors, you would prefer:

\( x^2 = 2x + 8 \) as it easily factors to \( (x - 4)(x + 2) = 0 \).