{"id":"cb_question_bank:339678fa-a69c-4c25-b55b-1768e27302d9","source_id":"cb_question_bank","source_item_id":"339678fa-a69c-4c25-b55b-1768e27302d9","external_id":null,"ibn":"034071-DC","question_id":"911383f2","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"What is the product of the solutions to the given equation?","stimulus":"open parenthesis, x minus 4, close parenthesis, times, open parenthesis, x plus 2, close parenthesis, times, open parenthesis, x minus 1, close parenthesis, equals 0","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2fa51a7739965e843aab0e22946bda987323c53a7c4831a20de5352e52646284\" alt=\"open parenthesis, x minus 4, close parenthesis, times, open parenthesis, x plus 2, close parenthesis, times, open parenthesis, x minus 1, close parenthesis, equals 0\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">What is the product of the solutions to the given equation?</p>\n","rationale_html":"<p>Choice D is correct. By the zero-product property, if <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/839505761ff21095acbfc5276b9bad8625131e8b5832c05f3f0c324b3d6cb10d\" alt=\"open parenthesis, x minus 4, close parenthesis, times, open parenthesis, x plus 2, close parenthesis, times, open parenthesis, x minus 1, close parenthesis, equals 0\"></span>, then <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/226cb72e39552d3bfaff10b3c935388cce9b1cff4eec361001d256414e38cfdf\" alt=\"x minus 4, equals 0\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2926fee01c9065fde061db140aa4e31c57be5ab10863f9e25f245b59105a1a68\" alt=\"x plus 2, equals 0\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5263dc3a6fe5690fe9c6ab41ffc64c8fdeacc4d55faa0e053c52cccb0c306846\" alt=\"x minus 1, equals 0\"></span>. Solving each of these equations for <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8459940867df2424b2ca04535d90ef8626c207ae08e7866b5a032d922cc75eee\" alt=\"x\"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7d90bc5cab99d91a4fc94163803642158e44f5a08bde8400e28498891da16def\" alt=\"x equals 4\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0edd49746d3055df6f32b5efedf4de1882d140a0d4f3698f8fb73b2b3693633b\" alt=\"x equals negative 2\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e4319fe2c5755fc5aa3f69e1a43b989d061cbb17c450f24b51a6616f131de4b\" alt=\"x equals 1\"></span>. The product of these solutions is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/042480c4a7e3bfb90296ae9d6bb4bd60498e7a7127d46b15848c17ed56993f9c\" alt=\"4 times negative 2, times 1, equals negative 8\"></span>.</p><p>Choice A is incorrect and may result from sign errors made when solving the given equation. Choice B is incorrect and may result from finding the sum, not the product, of the solutions. Choice C is incorrect and may result from finding the sum, not the product, of the solutions in addition to making sign errors when solving the given equation.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.627000+00:00","source_updated_at":"2023-08-02T20:25:59.627000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph block_choice\">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3ff25cd07f13d09c066cd808b1b6e5abf292f9768fdeed188585ad5f1a52a4ff\" alt=\"8\"></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph block_choice\">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b35ae18904fb781bd47e663cf02b992965491e4f50b31194e7d69870143879cd\" alt=\"3\"></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph block_choice\">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b62558094601a23d6fe95ffbc037ca0c41dd10264b6e51f4163b9ed575c135a3\" alt=\"negative 3\"></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph block_choice\">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0074a4418aa88cd673760d477e8b81bfb5e2a1a048bed34062ed94e05b6de763\" alt=\"negative 8\"></span></p>\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}}