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The function f is defined by a polynomial. Some values of x and f(x) are shown in the table above. Which of the following must be a factor of f(x) ?
  • a)
    x − 2
  • b)
    x − 3
  • c)
    x − 4
  • d)
    x − 5
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The function f is defined by a polynomial. Some values of x and f(x) a...
Choice C is correct. If x − b is a factor of f(x), then f(b) must equal 0. Based on the table, f(4) = 0. Therefore, x − 4 must be a factor of f(x).
Choice A is incorrect because f(2) ≠ 0; choice B is incorrect because no information is given about the value of f(3), so x − 3 may or may not be a factor of f(x); and choice D is incorrect because f(5) ≠ 0.
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Most Upvoted Answer
The function f is defined by a polynomial. Some values of x and f(x) a...
Choice C is correct. If x − b is a factor of f(x), then f(b) must equal 0. Based on the table, f(4) = 0. Therefore, x − 4 must be a factor of f(x).
Choice A is incorrect because f(2) ≠ 0; choice B is incorrect because no information is given about the value of f(3), so x − 3 may or may not be a factor of f(x); and choice D is incorrect because f(5) ≠ 0.
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The function f is defined by a polynomial. Some values of x and f(x) are shown in the table above. Which of the following must be a factor of f(x) ?a)x − 2b)x − 3c)x − 4d)x − 5Correct answer is option 'C'. Can you explain this answer?
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