# What are the zeros of #f(x) = 5x^7 − x + 216#?

##### 1 Answer

The first attempt to do is to *try* to factor that polinomy.

For the remainder theorem we have to calculate **this** is a zero.

The divisors are:

I tried some small of them, that did't work, and the other were too big.

So this polinomy can't be factorized.

We have to try another way!

Let's try to study the function.

The domain is

and so, there are not asymptotes of any type (obliqual, horizontal or vertical).

The derivative is:

and let's study the sign:

(the numbers are

so the function growths before

So: the point

Since their ordinate are positive, these point are **over** the x-axis,

so the function cuts the x-axis in only one point, as you can see:

graph{5x^7-x+216 [-34.56, 38.5, 199.56, 236.1]}

graph{5x^7-x+216 [-11.53, 10.98, -2.98, 8.27]}

So there is only one zero!