{"id":"cb_question_bank:cf757490-9cdb-410f-9870-e4c4fd0926e2","source_id":"cb_question_bank","source_item_id":"cf757490-9cdb-410f-9870-e4c4fd0926e2","external_id":null,"ibn":"021312-DC","question_id":"9f2ecade","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The function h is defined above, where a , b , and c are integer constants. If the zeros of the function are negative 5 6, and 7, what is the value of c ?","stimulus":"h of x equals, x cubed plus, a, x squared, plus b x, plus c","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/392141492b6f80d343fa5553abe80604cdeb057e6d315edf14e92b89078b01d9\" alt=\"h of x equals, x cubed plus, a, x squared, plus b x, plus c\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">The function <span class=\"italic\">h</span> is defined above, where <span class=\"italic\">a</span>, <span class=\"italic\">b</span>, and <span class=\"italic\">c</span> are integer constants. If the zeros of the function are <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6474b07df0e820f60a423fe70726c73b64d5091a22b8a1fcf0dc1adb650b31a1\" alt=\"negative 5\"></span></span> 6, and 7, what is the value of <span class=\"italic\">c </span>?</p>\n","rationale_html":"<p>The correct answer is 210. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8d84f0934ecb7d96090b9c086b990db006ef3ed6d80c6aa9d1f4b6324479d5b8\" alt=\"negative 5\"></span>, 6, and 7 are zeros of the function, the function can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7828bc29ee09d1cfd74cb160231808a2018d0fd5cdb90c13cf0bf3f105050570\" alt=\"h of x equals, open parenthesis, x plus 5, close parenthesis, times, open parenthesis, x minus 6, close parenthesis, times, open parenthesis, x minus 7, close parenthesis\"></span>. Expanding the function yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/81e79c849af198cd9b588958b9365a9ff2abb32ab9f50f5ad3ef7a16c1857c7c\" alt=\"h of x equals, x cubed, minus 8, x squared, minus 23 x, plus 210\"></span>. Thus, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/08aacb78d535f31a4261c7ca5d048758a9e35aba187dc420cb55debbad0c08af\" alt=\"a, equals negative 8\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/131cdb215328531ea62df484aae5bc833ad21e98726e659a270fc0cf7a52499b\" alt=\"b equals negative 23\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8740667ea440b99bef43176c9cea2ede71145892fbe35bce124c209ad765489c\" alt=\"c equals 210\"></span>. Therefore, the value of <span class=\"italic\">c</span> is 210.</p>\n","correct_answer":["210"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.616000+00:00","source_updated_at":"2023-08-02T20:25:59.616000+00:00","options":[],"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}}