6
advanced-math

Factor completely: 2x2182x^2 - 18

A

2(x3)22(x - 3)^2

B

2(x3)(x+3)2(x - 3)(x + 3)

C

(2x6)(x+3)(2x - 6)(x + 3)

D

(2x9)(x+2)(2x - 9)(x + 2)

Correct Answer: B

Choice B is the correct answer. Always factor out the GCF first.

  1. Factor out 2: 2(x29)2(x^2 - 9).
  2. Recognize that x29x^2 - 9 is a difference of squares.
  3. Factor x29x^2 - 9 into (x3)(x+3)(x - 3)(x + 3).

Final answer: 2(x3)(x+3)2(x - 3)(x + 3).

Choice A is incorrect because (x3)2(x-3)^2 expands to x26x+9x^2 - 6x + 9, which has a middle term. Choice C is incorrect because while mathematically equivalent, it is not completely factored (the first factor 2x62x-6 still has a GCF of 2). Choice D is incorrect because it doesn't expand to the original expression.