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

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

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

−12=x2−x

Answer 1

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

1. \( x^2 + 9x = 8 \)

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

2. \( x^2 = 2x + 8 \)

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

3. \( x^2 = 4x - 10 \)

   • Rearranging gives: \( x^2 - 4x + 10 = 0 \)
   • This does not factor nicely over the real numbers.

4. \( -12 = x^2 - x \)

   • Rearranging gives: \( x^2 - x + 12 = 0 \)
   • This does not factor nicely over the real numbers.

Thus, the equations that can be solved by factoring are:

• \( x^2 + 9x - 8 = 0 \)
• \( x^2 - 2x - 8 = 0 \)

In conclusion, the proper responses are:

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