COMPATIBILITY OF ALGEBRAIC AND VISUAL APPROACHES IN SOLVING 3RD AND 4TH ORDER EQUATIONS

The article analyzes a methodology for teaching third- and fourth-degree algebraic equations in which algebraic methods are employed as the primary instructional approach, while visual tools are used as auxiliary instruments. Students often encounter difficulties when searching for rational roots and applying Horner’s scheme in solving higher-degree equations. In the study, algebraic methods are considered the main teaching mechanism, whereas GeoGebra is treated as a tool for verifying and reinforcing algebraic solutions. The proposed step-by-step model emphasizes thorough instruction in algebraic methods at the initial stage, followed by visual verification to consolidate the results. Such an approach serves as an effective means of developing students’ functional thinking, enhancing their ability to independently identify errors, and fostering mathematical intuition.