Given a polynomial f(x), if (x − 3) is a factor, what else must be true? f(3) = 0
f(−3) = 0
f(0) = 3
f(0) = −3

A

Step-by-step explanation:

Recall that according to the Polynomial Remainder Theorem, if we divide a polynomial f(x) by a binomial in the form (x - a), then the remainder will be f(a).

And by the Factor Theorem, in order for a binomial (x - a) to be a factor of a polynomial f(x), the remainder must be 0. In other words, f(a) = 0.

We are given a polynomial f(x) and that (x - 3) is a factor.

Therefore, a = 3.

And since it is a factor, by the Factor Theorem, the remainder must be 0.

Therefore:

The answer is A.

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