4x^2 + − 45 The expression bx, where b is a constant, can be rewritten as (hx + k)(x + j), where h, k, and j are integer constants. Which of the following must be an integer?
Correct answer: D (parsed from the explanation — this source omits an answer key for this item)
Explanation
2+ - Choice D is correct. It’s given that 4x bx 45 can be rewritten as ( + )( + ) ( + )( + ) hx k x j . The expression hx k x j can be rewritten as 2+ + + 2+( + ) + 2+( + ) + hx jhx kx kj, or hx jh k x kj. Therefore, hx jh k x kj is 2+ - =- equivalent to 4x bx 45. It follows that kj 45. Dividing each side of this - = 45 -45 equation by k yields j . Since j is an integer, must be an integer. k k 45 Therefore, must also be an integer. k 40 SAT PRACTICE TEST #4 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS nnn MATH: MODULE 1 Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.
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