Hello, cityismine!
Use synthetic division to show that all of the real zeros of
lie in the interval I'm not sure why Synthetic Divison is used here . . .
We find that: .
. . The graph is below the xaxis.
We find that: .
. . The graph is above the xaxis.
We find that: .
. . The graph is below the xaxis.
We find that:.
. . The graph is above the xaxis.
So far, the graph looks like this: Code:

 (4,5)
(0,5)* *
 :
2  2 :
++++
:  : 4
:  :
:  :
*  *
(2,7)  (2,7}

Since a polynomial function is continuous, the graph must cross the xaxis
. . on the intervals
And those are the three (real) zeros of the cubic function. Code:

* *
*  * :
2  2 :
+o+o+o+
:  : 4
:  : *
: *  * : *
*  *
