{"id":"cb_question_bank:12b4e8a6-e7d5-4acc-9336-0f87f6f44eb1","source_id":"cb_question_bank","source_item_id":"12b4e8a6-e7d5-4acc-9336-0f87f6f44eb1","external_id":null,"ibn":"11189-DC","question_id":"371cbf6b","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The equation above is true for all x , where a and b are constants. What is the value of ab ?","stimulus":"open parenthesis, a x plus 3, close parenthesis, times, open parenthesis, 5 x squared, minus b x, plus 4, close parenthesis, equals, 20 x cubed, minus 9 x squared, minus 2 x, plus 12","stimulus_html":"
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\n \n \"open\n

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The equation above is true for all x, where a and b are constants. What is the value of ab ?

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Choice C is correct. If the equation is true for all x, then the expressions on both sides of the equation will be equivalent. Multiplying the polynomials on the left-hand side of the equation gives \"5. On the right-hand side of the equation, the only \"x-term is \"negative. Since the expressions on both sides of the equation are equivalent, it follows that \"negative, which can be rewritten as \"open. Therefore, \"negative, which gives \"a,.

Choice A is incorrect. If \"a,, then the coefficient of \"x on the left-hand side of the equation would be \"negative, which doesn’t equal the coefficient of \"x, \"negative, on the right-hand side. Choice B is incorrect. If \"a,, then the coefficient of \"x on the left-hand side of the equation would be \"negative, which doesn’t equal the coefficient of \"x, \"negative, on the right-hand side. Choice D is incorrect. If \"a,, then the coefficient of \"x on the left-hand side of the equation would be \"negative, which doesn’t equal the coefficient of \"x, \"negative, on the right-hand side.

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18

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20

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24

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40

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