{"id":"cb_practice_pdf:t10-math-m2-q25","source_id":"cb_practice_pdf","source_item_id":"t10-math-m2-q25","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-10","module_number":2,"position":25,"stem":"Which of the following expressions has a factor of x+2b, where b is a positive integer constant? 3x^2 +7x+14b","stimulus":"","stimulus_html":null,"stem_html":"<p>Which of the following expressions has a factor of x+2b, where b is a positive integer constant? 3x^2 +7x+14b</p>","rationale_html":"<p>3 2 Choice D is correct. Since each choice has a term of x , which can be written as 14 7 2 ^3xh^xh, and each choice has a term of b, which can be written as ^ h^ bh, the + expression that has a factor of x 2b, where b is a positive integer constant, can 3 +7 +2 be represented as ^ x h^x bh. Using the distributive property of 3 +2 +7 +2 multiplication, this expression is equivalent to x^x bh ^x bh, or 3 2+6 +7 +14 x xb x b. Combining the x-terms in this expression yields 3 2+ 7+6 +14 x ^ bhx b. It follows that the coefficient of the x-term is equal to 7+6 7+6 28 42 49 b. Thus, from the given choices, b must be equal to 7, , , or . 21 35 42 Therefore, 6b must be equal to 0, , , or , respectively, and b must be equal 0 21 35 42 42 to 6, 6, 6, or 6, respectively. Of these four values of b, only 6, or 7, is a 7+6 49 positive integer. It follows that b must be equal to because this is the only choice for which the value of b is a positive integer constant. Therefore, the + 3 2+49 +14 expression that has a factor of x 2b is x x b. + Choice A is incorrect. If this expression has a factor of x 2b, then the value of b is 0, which isn’t positive. Choice B is incorrect. If this expression has a factor of 21 + x 2b, then the value of b is 6, which isn’t an integer. Choice C is incorrect. If 35 + this expression has a factor of x 2b, then the value of b is 6, which isn’t an integer.</p>","correct_answer":["D"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>3x^2 +28x+14b</p>","ord":0},{"label":"B","content_html":"","ord":1},{"label":"C","content_html":"<p>3x^2 +42x+14b 3x^2 +49x+14b</p>","ord":2},{"label":"D","content_html":"","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}}