Explanation
Correct answer: C.
Choice C is correct. If the equation is true for all , then the expressions on both sides of the equation will be equivalent. Multiplying the polynomials on the left-hand side of the equation gives . On the right-hand side of the equation, the only -term is . Since the expressions on both sides of the equation are equivalent, it follows that , which can be rewritten as . Therefore, , which gives .
Why the other choices are wrong
Choice A
Choice A is incorrect. If , then the coefficient of on the left-hand side of the equation would be , which doesn't equal the coefficient of , , on the right-hand side.
Choice B
Choice B is incorrect. If , then the coefficient of on the left-hand side of the equation would be , which doesn't equal the coefficient of , , on the right-hand side.
Choice D
Choice D is incorrect. If , then the coefficient of on the left-hand side of the equation would be , which doesn't equal the coefficient of , , on the right-hand side.
Student discussion
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