General form of a factorable polynomial
This paper provides extension to the types of factoring of polynomials to illustrate the fact that multiplication with polynomials has no restrictions when it comes to the number of terms so does factoring. It aims to develop students’ perception about polynomials and to motivate them to continue discovering factorable polynomials.that are new to us.The idea originated from the expression x4 + x2 y2 + y4 which is a product of x2 + xy + y2 and x2 – xy + y2. Factor theorem, rational zeros of a polynomial, and symmetric and transitive properties of real numbers were used in this study in proving other factorable polynomials. The contents include the difference of perfect nth powers (ax)n – (by)n, the trinomial of the form xn + (xy)n/2 + yn, and the general form of a factorable polynomial p(x) = xn + xn – d yd + xn – 2d y2d + … + x2dyn – 2d + xdyn – d + yn for some positive integers n and d with a and b as real numbers.
Leithold, Louis. (1992). College Algebra and Trigonometry, (pp. 590, 597 – 604). Canada: Addison – Wesley Publishing Co., Inc.
This work is licensed under a Creative Commons Attribution 4.0 International License.