{"id":"cb_question_bank:14c2ac3b-aab7-4ff3-900d-48cc1692f527","source_id":"cb_question_bank","source_item_id":"14c2ac3b-aab7-4ff3-900d-48cc1692f527","external_id":null,"ibn":"08064-DC","question_id":"a05bd3a4","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following expressions is equivalent to x squared minus 5 ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Which of the following expressions is equivalent to <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/45f888f9324821db675190e5c57c6eae0d862fca662efc749049b8425d32c6d3\" alt=\"x squared minus 5\"></span></span> ?</p>\n","rationale_html":"<p>Choice C is correct. The expression can be written as a difference of squares&nbsp;<span class=\"italic\">x</span><sup>2</sup>&nbsp;–&nbsp;<span class=\"italic\">y</span><sup>2</sup>, which can be factored as (<span class=\"italic\">x</span>&nbsp;+&nbsp;<span class=\"italic\">y</span>)(<span class=\"italic\">x</span>&nbsp;–&nbsp;<span class=\"italic\">y</span>). Here,&nbsp;<span class=\"italic\">y</span><sup>2</sup>&nbsp;= 5, so&nbsp;<span class=\"italic\"></span><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c6e41bae5b266a1976d2d3998963d935a819cf0d9a8fc569ae4f33617b1d30f4\" alt=\"y equals the square root of 5\"></span>, and the expression therefore factors as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7bf389c8b905e15163818280c6cfd06593d161f12da91de1b8ab1d85c9d7ba56\" alt=\"open parenthesis, x plus the square root of 5, close parenthesis, times, open parenthesis, x minus the square root of 5, close parenthesis\"></span>.</p><p>Choices A and B are incorrect and may result from misunderstanding how to factor a difference of squares. Choice D is incorrect; (<span class=\"italic\">x</span>&nbsp;+ 5)(<span class=\"italic\">x</span>&nbsp;– 1) can be rewritten as <span class=\"italic\">x</span><sup>2</sup>&nbsp;+ 4<span class=\"italic\">x</span>&nbsp;– 5, which is not equivalent to the original expression.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.634000+00:00","source_updated_at":"2023-08-02T20:25:59.634000+00:00","options":[{"label":"A","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/54b57d0e3eeba6709899df925fc87660fca532eb04b36aa8d7afc0d6e1a36db2\" alt=\"open parenthesis, x plus the square root of 5, close parenthesis, squared\"></span></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/eb9327d25ee641f58d34bebb1c14f763b78b70be38d08243e520e5f116052977\" alt=\"open parenthesis, x minus the square root of 5, close parenthesis, squared\"></span></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/41f2a1072a4df7a9baf9c551330d98416af8b83c3a72408e21cb415527fa1d0d\" alt=\"open parenthesis, x plus the square root of 5, close parenthesis, times, open parenthesis, x minus the square root of 5, close parenthesis\"></span></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8c152b1bb9a3422f7ffe0880888ccfd4ad3ec46182598e454c341f767888765e\" alt=\"open parenthesis, x plus 5, close parenthesis, times, open parenthesis, x minus 1, close parenthesis\"></span></span>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}