4
advanced-math

Solve for xx: x24x=0x^2 - 4x = 0

A

x=4x = 4 only

B

x=0,4x = 0, 4

C

x=0,4x = 0, -4

D

x=2,2x = 2, -2

Correct Answer: B

Choice B is the correct answer. This equation can be solved by factoring out the Greatest Common Factor (GCF).

  1. Identify the GCF of x2x^2 and 4x-4x, which is xx.
  2. Factor out xx: x(x4)=0x(x - 4) = 0.
  3. Set each factor to zero: x=0x = 0 or x4=0x - 4 = 0.
  4. Solve: x=0x = 0 or x=4x = 4.

Choice A is incorrect because it misses the solution x=0x=0. Dividing both sides by xx is invalid because xx could be zero. Choice C is incorrect because x4=0x-4=0 gives x=4x=4, not -4. Choice D is incorrect because this would be the solution for x24=0x^2 - 4 = 0 (Difference of Squares).