{"id":"cb_question_bank:61dfa97b-4a3f-4a3a-9330-43ce655bbc1f","source_id":"cb_question_bank","source_item_id":"61dfa97b-4a3f-4a3a-9330-43ce655bbc1f","external_id":"21bb428c-50de-4b82-ba02-72c7b6db2d11","ibn":null,"question_id":"4a5af623","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which expression is a factor of 2 x squared plus 38 x plus 10 ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Which expression is a factor of <math alttext=\"2 x squared plus 38 x plus 10\"><mrow>\n\t<mrow>\n\t\t<mn>2</mn>\n\t\t<msup>\n\t\t\t<mi>x</mi>\n\t\t\t<mn>2</mn>\n\t\t</msup>\n\t</mrow>\n\t<mo>+</mo>\n\t<mrow>\n\t\t<mn>38</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>10</mn>\n</mrow>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. Since <math alttext=\"2\"><mn>2</mn>\n</math> is a common factor of each of the terms in the given expression, the expression can be rewritten as <math alttext=\"2 left parenthesis x squared plus 19 x plus 5 right parenthesis\"><mn>2</mn><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>19</mn><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced></math>. Therefore, the factors of the given expression are <math alttext=\"2\"><mn>2</mn>\n</math> and <math alttext=\"x squared plus 19 x plus 5\"><mrow>\n\t<msup>\n\t\t<mi>x</mi>\n\t\t<mn>2</mn>\n\t</msup>\n\t<mo>+</mo>\n\t<mrow>\n\t\t<mn>19</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>5</mn>\n</mrow>\n</math>. Of these two factors, only <math alttext=\"2\"><mn>2</mn>\n</math> is listed as a choice.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This is a term of the given expression, not a factor of the given expression.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This is a term of the given expression, not a factor of the given expression.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.821000+00:00","source_updated_at":"2023-08-02T20:25:59.821000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"2\"><mn>2</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"5 x\"><mrow>\n\t<mn>5</mn>\n\t<mi>x</mi>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"38 x\"><mrow>\n\t<mn>38</mn>\n\t<mi>x</mi>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"2 x squared\"><mrow>\n\t<mn>2</mn>\n\t<msup>\n\t\t<mi>x</mi>\n\t\t<mn>2</mn>\n\t</msup>\n</mrow>\n</math></p>","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}}