The expression 1/3x2 - 2 can be rewritten as 1/3 (x - k)(x + k), where k is a positive constant. What is the value of k?
Correct answer: D. √6
- A. 2
- B. 6
- C. √2
- D. √6
Explanation
Choice D is correct. Start by factoring the expression: 1/3 (x2 − 6). Recognize that x2 − 6 is a difference of squares, allowing it to be expressed as (x − √6)(x + √6). Therefore, k must be √6. Choice A is incorrect because it leads to a different constant term. Choice B results from an incorrect factorization, and Choice C arises from a misunderstanding of the expression being factored.
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