We find several applications of the Dynamic System Geogebra--DSG related predominantly to the basic mathematical concepts at the context of the learning and teaching in Brasil. However, all these works were developed in the basic level of Mathematics. On the other hand, we discuss and explore, with DSG's help, some applications of the polynomial's resultant at the academic level. In this context, we have the opportunity to identify certain limitations of this software. In fact, when we consider the Algebraic Geometry (AG), some analytical methods permit to describe when two plane algebraic curves "f" and "g" have a common factor. So, we will show some cases that the CAS Maple is necessary too for providing some conclusive dates. Finally, with this example, we wish to describe/systematize and structure a proposal of a Computation Technique for Teaching Mathematics (CTTM) in the academic level.