{"id":"cb_question_bank:fcd84555-5e4a-4723-a4a3-da174bb334b0","source_id":"cb_question_bank","source_item_id":"fcd84555-5e4a-4723-a4a3-da174bb334b0","external_id":"f0feb4ae-ee24-4b97-b265-104550acbce4","ibn":null,"question_id":"5d93c782","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which expression is equivalent to x squared plus 3 x minus 40 ?","stimulus":"","stimulus_html":null,"stem_html":"<p>Which expression is equivalent to <math alttext=\"x squared plus 3 x minus 40\"><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>3</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>-</mo>\n\t<mn>40</mn>\n</mrow>\n</math>?</p>","rationale_html":"<p>Choice B is correct. The given expression may be rewritten as <math alttext=\"x squared plus 8 x minus 5 x minus 40\"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>8</mn><mi>x</mi><mo>-</mo><mn>5</mn><mi>x</mi><mo>-</mo><mn>40</mn></math>. Since the first two terms of this expression have a common factor of <math alttext=\"x\"><mi>x</mi>\n</math> and the last two terms of this expression have a common factor of <math alttext=\"negative 5\"><mo>-</mo><mn>5</mn>\n</math>, this expression may be rewritten as <math alttext=\"x left parenthesis x right parenthesis plus x left parenthesis 8 right parenthesis minus 5 left parenthesis x right parenthesis minus 5 left parenthesis 8 right parenthesis\"><mi>x</mi><mfenced><mi>x</mi></mfenced><mo>+</mo><mi>x</mi><mfenced><mn>8</mn></mfenced><mo>-</mo><mn>5</mn><mfenced><mi>x</mi></mfenced><mo>-</mo><mn>5</mn><mfenced><mn>8</mn></mfenced></math>,&nbsp;or <math alttext=\"x left parenthesis x plus 8 right parenthesis minus 5 left parenthesis x plus 8 right parenthesis\"><mi>x</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfenced><mo>-</mo><mn>5</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfenced></math>. Since each term of this expression has a common factor of&nbsp;<math alttext=\"left parenthesis x plus 8 right parenthesis\"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfenced></math>, it may be rewritten as&nbsp;<math alttext=\"left parenthesis x minus 5 right parenthesis left parenthesis x plus 8 right parenthesis\"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfenced></math>.</p>\n<p>Alternate approach: An expression of the form&nbsp;<math alttext=\"x squared plus b x plus c\"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></math>, where <math alttext=\"b\"><mi>b</mi>\n</math> and <math alttext=\"c\"><mi>c</mi>\n</math> are constants, can be factored if there are two values that add to give <math alttext=\"b\"><mi>b</mi>\n</math> and multiply to give <math alttext=\"c\"><mi>c</mi>\n</math>. In the given expression, <math alttext=\"b equals 3\"><mi>b</mi><mo>=</mo><mn>3</mn></math> and&nbsp;<math alttext=\"c equals negative 40\"><mi>c</mi><mo>=</mo><mo>-</mo><mn>40</mn></math>. The values of <math alttext=\"negative 5\"><mo>-</mo><mn>5</mn>\n</math> and <math alttext=\"8\"><mn>8</mn>\n</math> add to give <math alttext=\"3\"><mn>3</mn>\n</math> and multiply to give <math alttext=\"negative 40\"><mo>-</mo><mn>40</mn>\n</math>, so the expression can be factored as <math alttext=\"left parenthesis x minus 5 right parenthesis left parenthesis x plus 8 right parenthesis\"><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>8</mn></mrow></mfenced></math>.</p>\n<p>Choice A is incorrect. This expression is equivalent to&nbsp;<math alttext=\"x squared plus 6 x minus 40\"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mi>x</mi><mo>-</mo><mn>40</mn></math>, not <math alttext=\"x squared plus 3 x minus 40\"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>40</mn></math>.</p>\n<p>Choice C is incorrect. This expression is equivalent to <math alttext=\"x squared minus 3 x minus 40\"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>40</mn></math>, not <math alttext=\"x squared plus 3 x minus 40\"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>40</mn></math>.</p>\n<p>Choice D is incorrect. This expression is equivalent to <math alttext=\"x squared minus 6 x minus 40\"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mi>x</mi><mo>-</mo><mn>40</mn></math>, not <math alttext=\"x squared plus 3 x minus 40\"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>40</mn></math>.</p>","correct_answer":["B"],"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=\"left parenthesis x minus 4 right parenthesis left parenthesis x plus 10 right parenthesis\"><mrow>\n\t<mfenced>\n\t\t<mrow>\n\t\t\t<mi>x</mi>\n\t\t\t<mo>-</mo>\n\t\t\t<mn>4</mn>\n\t\t</mrow>\n\t</mfenced>\n\t<mfenced>\n\t\t<mrow>\n\t\t\t<mi>x</mi>\n\t\t\t<mo>+</mo>\n\t\t\t<mn>10</mn>\n\t\t</mrow>\n\t</mfenced>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"left parenthesis x minus 5 right parenthesis left parenthesis x plus 8 right parenthesis\"><mrow>\n\t<mfenced>\n\t\t<mrow>\n\t\t\t<mi>x</mi>\n\t\t\t<mo>-</mo>\n\t\t\t<mn>5</mn>\n\t\t</mrow>\n\t</mfenced>\n\t<mfenced>\n\t\t<mrow>\n\t\t\t<mi>x</mi>\n\t\t\t<mo>+</mo>\n\t\t\t<mn>8</mn>\n\t\t</mrow>\n\t</mfenced>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"left parenthesis x minus 8 right parenthesis left parenthesis x plus 5 right parenthesis\"><mrow>\n\t<mfenced>\n\t\t<mrow>\n\t\t\t<mi>x</mi>\n\t\t\t<mo>-</mo>\n\t\t\t<mn>8</mn>\n\t\t</mrow>\n\t</mfenced>\n\t<mfenced>\n\t\t<mrow>\n\t\t\t<mi>x</mi>\n\t\t\t<mo>+</mo>\n\t\t\t<mn>5</mn>\n\t\t</mrow>\n\t</mfenced>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"left parenthesis x minus 10 right parenthesis left parenthesis x plus 4 right parenthesis\"><mrow>\n\t<mfenced>\n\t\t<mrow>\n\t\t\t<mi>x</mi>\n\t\t\t<mo>-</mo>\n\t\t\t<mn>10</mn>\n\t\t</mrow>\n\t</mfenced>\n\t<mfenced>\n\t\t<mrow>\n\t\t\t<mi>x</mi>\n\t\t\t<mo>+</mo>\n\t\t\t<mn>4</mn>\n\t\t</mrow>\n\t</mfenced>\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}}