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Set 5: Quadratic Equations (Intermediate)

Explanation

Answer: C

Factor: 16x2116x^2 - 1

A.

(4x1)2(4x - 1)^2

B.

(16x1)(x+1)(16x - 1)(x + 1)

C.

(4x1)(4x+1)(4x - 1)(4x + 1)

✓ Correct
D.

(8x1)(2x+1)(8x - 1)(2x + 1)

Detailed Explanation

Choice C is correct. Choice C is the correct answer. This is a difference of squares: (4x)212(4 x)^2 - 1^2. 1. a=4xa = 4 x, b=1b = 1. 2. Formula: (ab)(a+b)(a - b)(a + b). 3. Result: (4x1)(4x+1)(4 x - 1)(4 x + 1). Choice A is incorrect because it would have a middle term of 8x-8 x. Choice B is incorrect because it expands to 16x2+15x116x^2 + 15 x - 1. Choice D is incorrect because it expands to 16x2+6x116x^2 + 6 x - 1.

Key Steps:

The correct answer is (4x1)(4x+1)(4x - 1)(4x + 1)

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
B: Choice B is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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