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16 For the polynomial function f, the graph of = y f x in the xy-plane passes through the points ^ h -5,0, 1,0, and 4,0. Which of the following ^ h ^ h ^ h must be a factor of f x? ^ h
Correct answer: C (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice C is correct. It’s given that f is a polynomial function and the graph of = -5,0 1,0 4,0 y f^xh in the xy-plane passes through the points ^ h, ^ h, and ^ h. A ,0 - point in the form ^a h on the graph of f^xh means that x a is a factor of f^xh. 1,0 - Since the graph of the function f passes through the point ^ h, x 1 must be a factor of f^xh. = Choice A is incorrect. This is a factor if the graph of y f^xh passed through -1,0 = ^ h. Choice B is incorrect. This is a factor if the graph of y f^xh passed -4,0 = through ^ h. Choice D is incorrect. This is a factor if the graph of y f^xh 5,0 passed through ^ h.
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