Question Bank / Math / Equivalent Expressions

Equivalent expressions SAT question

Math · Advanced Math · Hard · Answer it here, explanation included.

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 ?

ExplanationShow

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 $one third times, open parenthesis, x squared, minus 2, close parenthesis$ .

Drill this skill on Aceit

Adaptive practice, a daily plan, and score tracking take a free account so we can save your work.

Practice this skill

Equivalent expressions SAT question

More Equivalent expressions questions