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

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

x2+9x=8

Answer 1

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

1. \(x^2 = 4x - 10\) \[ x^2 - 4x + 10 = 0 \] This does not factor nicely since the discriminant \(b^2 - 4ac = (-4)^2 - 4(1)(10) = 16 - 40 = -24\) is negative.

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

3. \(-12 = x^2 - x\) \[ x^2 - x + 12 = 0 \] This does not factor nicely since the discriminant \(b^2 - 4ac = (-1)^2 - 4(1)(12) = 1 - 48 = -47\) is negative.

4. \(x^2 + 9x = 8\) \[ x^2 + 9x - 8 = 0 \] This can also be factored as \((x + 8)(x - 1) = 0\).

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

• \(x^2 = 2x + 8\)
• \(x^2 + 9x = 8\)

So, the answers are:

• \(x^2 = 2x + 8\)
• \(x^2 + 9x = 8\)