Question

Question #490b3

Answer 1

Please see below.

Explanation:

.

A polynomial of degree `4` has a general form of:

`y=ax^4+bx^3+cx^2+dx+f`

It has four roots, i.e. if you solve for `x` you will have `4` answers. These roots, if they are all real numbers, are where the graph of this function crosses the `x`-axis.

So, you can pick `4` values of your choice between `-10` and `10` and make them the roots of your polynomial. Let's pick:

`x=-4, -1, 2, 5`

Then, you can write your function as follows:

`y=(x+4)(x+1)(x-2)(x-5)`

After multiplying them through and removing parentheses, you get:

`y=x^4-2x^3-21x^2+22x+40`

Here is its graph:

As you can see. the graph crosses the `x`-axis at the `x` values you picked.