The division of polynomials by monomials is relatively simple once you get the hang of it. Monomials consist of multiplied constants and variables with non-negative, whole number powers (for example, 4xyz^2, but not 3xyz^(-4/5) ). Polynomials are composed of multiple monomials added or subtracted together (for example, 4xyz^2 + xyz -- x^2yz).
(For these and all further examples, x, y, z, a, b, and c are all variables). Monomials can divide evenly into polynomials if the monomial is a factor of the terms of the polynomial. If it does not divide evenly, part or all of the monomial will be incorporated as a denominator of the then fractional terms of the polynomial.
Determine whether the monomial divisor shares a factor with the polynomial. For example, take: ( xy^4z^4 + x^2yz^3 + x^5y^3z ) / x^2y^2z^2abc Each term of the polynomial contains a factor of xyz. The polynomial can thus be factored into: ( xyz ) * ( y^3z^3 + xz^2 + x^4y^2 ) / ( xyz ) * ( xyzabc ) Then the division is ... more.
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