Consider the following polynomial.

F(x)=x^3+x^2−22x−40
Use synthetic division to identify integer bounds of the real zeros. Find the least upper bound and the greatest lower bound guaranteed by the Upper and Lower Bounds of Zeros theorem.

Upper Bound:
Lower Bound:

Question

Consider the following polynomial.

F(x)=x^3+x^2−22x−40
 Use synthetic division to identify integer bounds of the real zeros. Find the least upper bound and the greatest lower bound guaranteed by the Upper and Lower Bounds of Zeros theorem.

Upper Bound:
Lower Bound:

XioGonz · Answer

I found a video that may be quite helpful to you- https://m.youtube.com/watch?v=XgGzm0d_MDY

surjithayer · Answer

$$f(x)=x^3+x^2-22x-40$$
$$40=2\times2\times2\times5$$
$$factors  ~of~40~are~\pm 1,\pm 2,\pm 4,\pm5,\pm8,\pm10,\pm20,\pm 40$$
5| 1  1  -22    40
  | -   5   30 | -40
<hr class="bbcode_rule" />

|  1   6    8|0

$$x^2+6x+8=0$$
-2| 1   6   8
   |  -  -2  -8
 ____________
   | 1   4  |0
x+4=0
zeros are $$5,-4,-2$$
$$f(x)=x^3+x^2-22x+40=(x+2)(x+4)(x-5)$$