{"id":"cb_practice_pdf:t6-math-m1-q12","source_id":"cb_practice_pdf","source_item_id":"t6-math-m1-q12","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-6","module_number":1,"position":12,"stem":"Which expression is equivalent to +11^2 + x−5 x+5 x^2? +23x^2 −14","stimulus":"","stimulus_html":null,"stem_html":"<p>Which expression is equivalent to +11^2 + x−5 x+5 x^2? +23x^2 −14</p>","rationale_html":"<p>2+11 2 Choice B is correct. The expression ^x h can be written as 2+11 2+11 2 2+11+11 2+11 2 ^x h^x h, which is equivalent to x ^x h ^x h. Distributing x 2+11 4+11 2+11 2+121 4+22 2+121 and 11 to ^x h yields x x x , or x x . The - + - + - expression ^x 5h^x 5h is equivalent to ^x 5hx ^x 5h5. Distributing x and 5 - 2-5 +5 -25 2-25 to ^x 5h yields x x x , or x . Therefore, the expression 2+11 2+ -5 +5 4+22 2+121+ 2-25 ^x h ^x h^x h is equivalent to ^x x h ^x h, or 4+22 2+121+ 2-25 x x x . Combining like terms in this expression yields 4+23 2+96 x x . Choice A is incorrect. Equivalent expressions must be equivalent for any value of -14 x. Substituting 0 for x in this expression yields , whereas substituting 0 for 96 x in the given expression yields . Choice C is incorrect. Equivalent expressions must be equivalent for any value of x. Substituting 0 for x in this expression 121 96 yields , whereas substituting 0 for x in the given expression yields . Choice D is incorrect. Equivalent expressions must be equivalent for any value of 146 x. Substituting 0 for x in this expression yields , whereas substituting 0 for x 96 in the given expression yields .</p>","correct_answer":["B"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>x^4 +23x^2 +96</p>","ord":0},{"label":"B","content_html":"<p>x^4 +12x^2 +121</p>","ord":1},{"label":"C","content_html":"<p>x^4 +x^2 +146</p>","ord":2},{"label":"D","content_html":"<p>x^4</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}