sat suite question viewer

Advanced Math / Equivalent expressions Difficulty: Hard

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 ?

Back question 36 of 102 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

Explanation

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