In the expression above, b and c are positive integers. If the expression is equivalent to and , which of the following could be the value of c ?
A
4
B
6
C
8
D
10
Correct answer: A
Explanation
Choice A is correct. If the given expression is equivalent to , then , where x isn’t equal to b. Multiplying both sides of this equation by yields . Since the right-hand side of this equation is in factored form for the difference of squares, the value of c must be a perfect square. Only choice A gives a perfect square for the value of c.
Choices B, C, and D are incorrect. None of these values of c produces a difference of squares. For example, when 6 is substituted for c in the given expression, the result is . The expression can’t be factored with integer values, and therefore isn’t equivalent to .
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id cb_question_bank:33f9cecc-f6c4-432b-9b5b-995c8c45aae1 · question d8789a4c · IBN 028934-DC
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