The polynomials are not given, but we can answer in a general way.
Basically, what you need to test is:
Sign[p(-4)] ≠ Sign[p(-1)]
But let's see why.
The intermediate value theorem says that, if for two values a and b such that:
a < b
If we have a given continuous function such that:
f(a) < 0 and f(b) > 0.
or
f(a) > 0 and f(b) < 0
Then there exists a value c
a < c < b
Such that:
f(c) = 0
So to find the correct polynomial, you just need to evaluate it in both extremes of the interval and you should see that the sign changes.
This means that if p(x) is the polynomial, then you should have:
Sign[p(-4)] ≠ Sign[p(-1)]
This will imply, by the intermediate value theorem, that the polynomial is equal to zero for some given value on the given interval.
If you want to learn more, you can read:
https://brainly.com/question/23792383
