# How do you solve #x^4+8x^3+15x^2-4x-20<0#?

I would recommend first factoring and then selecting test points.

By the rational root theorem, a polynomial

There exists the remainder theorem to help us quickly sort out which are viable factors. For a polynomial

This can be a long process, but generally speaking, you find a factor within the first five tries if you go in increasing order. Starting at 1:

Hence,

So,

However, since we still have a polynomial of degree

So,

We can factor the trinomial as

Hence,

Selecting test points for x, you will find that

Here is the representation on a) a graph and on b) a number line.

Note: The line should be dotted in the graph (my graphing program cannot do this).

Hopefully this helps!

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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