{"id":"cb_practice_pdf:t4-math-m1-q23","source_id":"cb_practice_pdf","source_item_id":"t4-math-m1-q23","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":null,"form_id":"cb_practice_pdf:test-4","module_number":1,"position":23,"stem":"4x^2 + − 45 The expression bx, where b is a constant, can be rewritten as (hx + k)(x + j), where h, k, and j are integer constants. Which of the following must be an integer?","stimulus":"","stimulus_html":null,"stem_html":"<p>4x^2 + − 45 The expression bx, where b is a constant, can be rewritten as (hx + k)(x + j), where h, k, and j are integer constants. Which of the following must be an integer?</p>","rationale_html":"<p>2+ - Choice D is correct. It’s given that 4x bx 45 can be rewritten as ( + )( + ) ( + )( + ) hx k x j . The expression hx k x j can be rewritten as 2+ + + 2+( + ) + 2+( + ) + hx jhx kx kj, or hx jh k x kj. Therefore, hx jh k x kj is 2+ - =- equivalent to 4x bx 45. It follows that kj 45. Dividing each side of this - = 45 -45 equation by k yields j . Since j is an integer, must be an integer. k k 45 Therefore, must also be an integer. k 40 SAT PRACTICE TEST #4 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS nnn MATH: MODULE 1 Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.</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>b/h</p>","ord":0},{"label":"B","content_html":"<p>b/k</p>","ord":1},{"label":"C","content_html":"<p>45/h</p>","ord":2},{"label":"D","content_html":"<p>45/k</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}}