Error Analysis in the Resolutions of 1st Year High School Students in the Study of Notable Products and Polynomial Factoring

The present research had as objectives: to analyze successes and mistakes committed in the resolutions of 36 students of a class of the 1st year of High School, of a Pernambuco state school in the city of Petrolina; as well as, to present suggestions for investigations/ explorations, so that teachers who teach Mathematics can contemplate Error Analysis both in the methodological alternative of research, as in teaching, in Mathematical Education. For this aim, a student diagnostic questionnaire was proposed, from which 3 open questions were analyzed, the first sought to probe students' affirmations about the contents of polynomials and the last two of which dealt, in particular, with the contents of Notable Products and polynomial Factorization. From this analysis, 6 categories were created. By results, Categories D, C and B presented, respectively, the highest number of appearances, revealing a large number of mistakes in the distinction between polynomials and equations, in various algebraic manipulations and in the use of practical rules for the development of Notable Products.