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

Question

Responses

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

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

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

−12=x2−x

Answer 1

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

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

   Rearranging gives: \[ x^2 - 4x + 10 = 0 \]

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

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

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

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

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

   Rearranging gives: \[ x^2 - x + 12 = 0 \]

Now evaluating which of these equations can be factored:

• The first equation \(x^2 - 4x + 10 = 0\) does not have rational roots and cannot be factored.
• The second equation \(x^2 - 2x - 8 = 0\) can be factored as \((x - 4)(x + 2) = 0\).
• The third equation \(x^2 + 9x - 8 = 0\) can be factored as \((x + 8)(x - 1) = 0\).
• The fourth equation \(x^2 - x + 12 = 0\) does not have rational roots and cannot be factored.

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

• \(x^2 = 2x + 8\)
• \(x^2 + 9x = 8\)

So, the answers are:

• \(x^2 = 2x + 8\)
• \(x^2 + 9x = 8\)