{"id":"cb_question_bank:97d8de9b-f84e-4ce7-a7ce-31522efe3fd1","source_id":"cb_question_bank","source_item_id":"97d8de9b-f84e-4ce7-a7ce-31522efe3fd1","external_id":null,"ibn":"09133-DC","question_id":"f237ccfc","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":5,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The sum of negative 2 x squared, plus x, plus 31 and 3 x squared, plus 7 x, minus 8 can be written in the form a, x squared, plus b x, plus c , where a , b , and c are constants. What is the value of a, plus b plus c ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">The sum of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ad032733210bb0feabd668516918faaee24261d641e394f6401be38be7b46859\" alt=\"negative 2 x squared, plus x, plus 31\"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/22a0d044ebd15651cbe947f94b9a834bda68b4ac4afb3ad770e9b54ab09c2cc8\" alt=\"3 x squared, plus 7 x, minus 8\"></span></span> can be written in the form <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/934e21781a6f763f949024aa31fdfc0cda125720480046286c0b1333e65e0310\" alt=\"a, x squared, plus b x, plus c\"></span></span>, where <span class=\"italic\">a</span>, <span class=\"italic\">b</span>, and <span class=\"italic\">c</span> are constants. What is the value of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fa49fa50efdf9ec3a91b4284e8eae95150975104dad325741ac0671fdf23f042\" alt=\"a, plus b plus c\"></span></span> ?</p>\n","rationale_html":"<p>The correct answer is 32. The sum of the given expressions is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/efa6334d1284999abf4225d42ced6a2e18dc45199ac666c87583030e181894da\" alt=\"open parenthesis, negative 2, x squared, plus x, plus 31, close parenthesis, plus, open parenthesis, 3 x squared, plus 7 x, minus 8, close parenthesis\"></span>. Combining like terms yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4ee954f956568ed37e406b972c69339928b31ef7a3f433cc45400c445800a601\" alt=\"x squared, plus 8 x, plus 23\"></span>. Based on the form of the given equation, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/35066e9ba042cc64fd96f387da862ae288c94643a339ae4d2b59cd378d89d3a4\" alt=\"a, equals 1\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e8f75fe81e77755d032b007d4747840cfb2bd22bac91e1c1769cc4aaf1e9d38a\" alt=\"b equals 8\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7bbdc62429bce6fdaa2e6d44ca06e972a04b4c62c6c83fcb0e7ba0826d39de8f\" alt=\"c equals 23\"></span>. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/80010d81b8e8dbe9c35807ab54b336de96042ba056156be533048b1405649439\" alt=\"a, plus b, plus c, equals 32\"></span>.</p><p>Alternate approach: Because <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/071ba7e307586ef87ab6b1f3bd2a9f52a56b750873ce79dbe08acc0be82b5e39\" alt=\"a, plus b, plus c\"></span> is the value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/934e21781a6f763f949024aa31fdfc0cda125720480046286c0b1333e65e0310\" alt=\"a, x squared, plus b x, plus c\"></span> when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e4319fe2c5755fc5aa3f69e1a43b989d061cbb17c450f24b51a6616f131de4b\" alt=\"x equals 1\"></span>, it is possible to first make that substitution into each polynomial before adding them. When <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e4319fe2c5755fc5aa3f69e1a43b989d061cbb17c450f24b51a6616f131de4b\" alt=\"x equals 1\"></span>, the first polynomial is equal to<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/88b480341750d41e9aa91c8172b4d8310247ab7083ce33eef76693b3b958a2df\" alt=\"negative 2 plus 1, plus 31, equals 30\"></span> and the second polynomial is equal to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fe0bf82109f53f0f49640eb9887183e3c6699691a9d8143d4072e87ab19569ac\" alt=\"3 plus 7, minus 8, equals 2\"></span>. The sum of 30 and 2 is 32.</p><p></p>\n","correct_answer":["32"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.636000+00:00","source_updated_at":"2023-08-02T20:25:59.636000+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}}