{"id":"cb_question_bank:0660b69e-aff6-4c4f-b106-a9c49331bda7","source_id":"cb_question_bank","source_item_id":"0660b69e-aff6-4c4f-b106-a9c49331bda7","external_id":null,"ibn":"09342-DC","question_id":"dd4ab4c4","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 is a factor of the polynomial above?","stimulus":"4 a squared, plus 20 a b, plus 25 b squared","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/5f7051d7df7414097adc26e1d6629f9895eb488fdd3cef0a462c93ec3f5a7b54\" alt=\"4 a squared, plus 20 a b, plus 25 b squared\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following is a factor of the polynomial above?</p>\n","rationale_html":"<p>Choice B is correct. The first and last terms of the polynomial are both squares such that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4b80c9ad1994a02be38d7825250722225149c36cd9eea26cde73a94d7f57e946\" alt=\"4 a, squared, equals, open parenthesis, 2 a, close parenthesis, squared\"></span>&nbsp;and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/342afeaff36f174029316d86cea2ddc89cd700e1505a6dd3077e15c470842e03\" alt=\"25 b squared, equals, open parenthesis, 5 b, close parenthesis, squared\"></span><span class=\"italic\">. </span>The second term is twice the product of the square root of the first and last terms: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dcb91ce1a909428e69d31c88d4361d47ba7c42b05955a4cfe52e432617dee3dc\" alt=\"20 a, b, equals 2, times 2 a, times 5 b\"></span><span class=\"italic\">. </span>Therefore, the polynomial is the square of a binomial such that&nbsp;<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/72fee4aeebaa334b215a83b2ff581ab350dc946b4a5656df9bdfd547737980f4\" alt=\"4 a, squared, plus 20 a, b, plus 25 b squared, equals, open parenthesis, 2 a, plus 5 b, close parenthesis, squared\"></span>, and&nbsp;<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/121bf589d5e3acf7f50890a665f6e61d4ecc092396f99a7bf53cfef3b9d00b9e\" alt=\"open parenthesis, 2 a, plus 5 b, close parenthesis\"></span> is a factor.</p><p>Choice A is incorrect and may be the result of incorrectly factoring the polynomial. Choice C is incorrect and may be the result of dividing the second and third terms of the polynomial by their greatest common factor. Choice D is incorrect and may be the result of not factoring the coefficients.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.637000+00:00","source_updated_at":"2023-08-02T20:25:59.637000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/90874e3b35f41c70a9a76eeaad2ae42db3d2ec2cd0593c162905d714304e8b8d\" alt=\"a plus b\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/61e16da4de914ae10b1f47084a122ad5c5769fbe6d96335c81404f0b85d56bbd\" alt=\"2 a plus 5 b\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9152ad1d9ef14ec1c1640be9d03fe50988de0e59b06b14370954893f59f3e287\" alt=\"4 a plus 5 b\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d5d468d3af086350a0fee02d48e77ee790257148c1d5021fca35f2c7b8a6dc2d\" alt=\"4 a plus 25 b\"></span></span>\n          </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}}