What does this ellipsis mean?

[Mel Gibson]

Hello mathhelp, I'm currently reviewing for my midterms and am stuck on the following problem:
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Which zero listed below is not a possible zero of the equation y = 4x⁷+. . . . .-5x+10
a. 4
b.10
c. 2
d. 1
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I have two questions:
1. What does the ellipsis mean
2. How do I do it

Answer listed was 4 but I don't know how to get there.

Thanks in advance,
-Mel Gibson

 

[MarkFL]

Hello, and welcome to FMH!

1. The ellipsis just means there are some terms in the polynomial not listed. We don't need them to answer the question.

2. We can determine a list of possible zeroes using the rational Root Theorem:

Rational root theorem - Wikipedia

en.wikipedia.org

Using this theorem, we can see that 4 cannot be a rational root of the given polynomial, because 4 cannot be expressed as a factor of 10 divided by a factor of 4.