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

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
x squared plus 9 x equals 8
Remaining Attempts : 3

1 answer

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

  1. \(x^2 = 4x - 10\)
    Rearranging:
    \(x^2 - 4x + 10 = 0\)
    The discriminant (\(b^2 - 4ac\)) is \(16 - 40 = -24\) (not factorable).

  2. \(x^2 = 2x + 8\)
    Rearranging:
    \(x^2 - 2x - 8 = 0\)
    The discriminant is \(4 + 32 = 36\) (which is a perfect square: \(6^2\)). This can be factored as \((x - 4)(x + 2) = 0\).

  3. \(-12 = x^2 - x\)
    Rearranging:
    \(x^2 - x + 12 = 0\)
    The discriminant is \((-1)^2 - 4(1)(12) = 1 - 48 = -47\) (not factorable).

  4. \(x^2 + 9x = 8\)
    Rearranging:
    \(x^2 + 9x - 8 = 0\)
    The discriminant is \(81 + 32 = 113\) (not factorable).

From the analysis, the quadratic equation that can be solved by factoring is:

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