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.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

c. 1,233 miles