Question

If (X-5) is a factor of PCX), which of the following must be true?

A root of f(x) is x=-5.
A root of f(x) is x = 5.
Both x= -5 and x = 5 are roots of f(x).
Neither x = -5 nor x = 5 is a root of f(x).

Answer 1

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Answer:

A root of f(x) is x = 5

Explanation:

If (x -5) is a factor of f(x), then the value x=5 will make the function value be zero. That is, x=5 is a root of f(x).

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x = -5 may or may not be a root of f(x). The given information is insufficient for us to say that "x=-5 is a root" must be true.

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Additional explanation

If (x-5) is a factor of f(x), then we can write f(x) as ...

f(x) = (x -5)q(x) . . . . . for some polynomial q(x)

Then ...

f(5) = (5 -5)q(5) = 0·q(5) = 0 . . . . . without regard to the value of q(5)

f(5) = 0 means 5 is a root of f(x)