{"id":"cb_question_bank:40efbc46-80c9-4125-b0a0-c9c8f94bb439","source_id":"cb_question_bank","source_item_id":"40efbc46-80c9-4125-b0a0-c9c8f94bb439","external_id":"4d5ada3e-eaea-405e-9b02-b7797ddf34f3","ibn":null,"question_id":"c303ad23","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":"H","score_band":7,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If 3 x squared minus 18 x minus 15 equals 0 , what is the value of x squared minus 6 x ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">If <math alttext=\"3 x squared minus 18 x minus 15 equals 0\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>3</mn>\n\t\t\t<msup>\n\t\t\t\t<mi>x</mi>\n\t\t\t\t<mn>2</mn>\n\t\t\t</msup>\n\t\t</mrow>\n\t\t<mo>-</mo>\n\t\t<mrow>\n\t\t\t<mn>18</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>-</mo>\n\t\t<mn>15</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>, what is the value of <math alttext=\"x squared minus 6 x\"><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>6</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n</mrow>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"5\"><mn>5</mn>\n</math>. Dividing each side of the given equation by <math alttext=\"3\"><mn>3</mn>\n</math>&nbsp;yields <math alttext=\"x squared minus 6 x minus 5 equals 0\"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mi>x</mi><mo>-</mo><mn>5</mn><mo>=</mo><mn>0</mn></math>. Adding <math alttext=\"5\"><mn>5</mn>\n</math> to each side of this equation yields <math alttext=\"x squared minus 6 x equals 5\"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mi>x</mi><mo>=</mo><mn>5</mn></math>. Therefore, if <math alttext=\"3 x squared minus 18 x minus 15 equals 0\"><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>18</mn><mi>x</mi><mo>-</mo><mn>15</mn><mo>=</mo><mn>0</mn></math>,&nbsp;the value of <math alttext=\"x squared minus 6 x\"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mi>x</mi></math> is <math alttext=\"5\"><mn>5</mn>\n</math>.</p>","correct_answer":["5"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.823000+00:00","source_updated_at":"2023-08-02T20:25:59.823000+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}}