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Test
Math
Domain
Advanced Math
Skill
Equivalent expressions
Difficulty
Medium
ID: a05bd3a4
Modded SAT Question Bank by Abdullah Mallik

Which of the following expressions is equivalent to x squared minus 5 ?

  1. open parenthesis, x plus the square root of 5, close parenthesis, squared
  2. open parenthesis, x minus the square root of 5, close parenthesis, squared
  3. open parenthesis, x plus the square root of 5, close parenthesis, times, open parenthesis, x minus the square root of 5, close parenthesis
  4. open parenthesis, x plus 5, close parenthesis, times, open parenthesis, x minus 1, close parenthesis
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Correct Answer: C
Rationale

Choice C is correct. The expression can be written as a difference of squares x2 – y2, which can be factored as (x + y)(x – y). Here, y2 = 5, so y equals the square root of 5, and the expression therefore factors as open parenthesis, x plus the square root of 5, close parenthesis, times, open parenthesis, x minus the square root of 5, close parenthesis.

Choices A and B are incorrect and may result from misunderstanding how to factor a difference of squares. Choice D is incorrect; (x + 5)(x – 1) can be rewritten as x2 + 4x – 5, which is not equivalent to the original expression.

Question Difficulty: Medium
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