In the expression above, b and c are positive integers. If the expression is equivalent to and , which of

Question

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 ?

Accepted Answer

Choice A is correct. If the given expression is equivalent to , then , where x isn&rsquo;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&rsquo;t be factored with integer values, and therefore isn&rsquo;t equivalent to .

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