Question #a0b4103e - SAT Suite Question Bank

ID: a0b4103e

Modded SAT Question Bank by Abdullah Mallik

The expression $one-third x squared, minus 2$ can be rewritten as $one-third times, open parenthesis, x minus k, close parenthesis, times, open parenthesis, x plus k, close parenthesis$ , where k is a positive constant. What is the value of k ?

2
6
$the square root of 2$
$the square root of 6$

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Correct Answer: D

Rationale

Choice D is correct. Factoring out the coefficient $one third$ , the given expression can be rewritten as $one third times, open parenthesis, x squared, minus 6, close parenthesis$ . The expression $x squared, minus 6$ can be approached as a difference of squares and rewritten as $open parenthesis, x minus the square root of 6, close parenthesis, times, open parenthesis, x plus the square root of 6, close parenthesis$ . Therefore, k must be $the square root of 6$ .

Choice A is incorrect. If k were 2, then the expression given would be rewritten as $one third times, open parenthesis, x minus 2, close parenthesis, times, open parenthesis, x plus 2, close parenthesis$ , which is equivalent to $one third, x squared, minus four thirds$ , not $one third, x squared, minus 2$ .

Choice B is incorrect. This may result from incorrectly factoring the expression and finding $open parenthesis, x minus 6, close parenthesis, times, open parenthesis, x plus 6, close parenthesis$ as the factored form of the expression. Choice C is incorrect. This may result from incorrectly distributing the $one third$ and rewriting the expression as $one third times, open parenthesis, x squared, minus 2, close parenthesis$ .

Question Difficulty: Hard