Question 934535
if polynomials are closed under division, then the answer must also be a polynomial.


a polynomial must have all variables raised to a non-negative integer.


x^3/x^6 = x^-3 which is not a polynomial because the exponent of the variable is negative.


(x^6) / (3x^2) = (x^4)/3 which is a polynomial because the exponent of the variable is a non-negative integer.


(x^4 - 121) / (x - 121) results in x^3 + 121x^2 + 121^2x + 121^3 + (121^4-121)/(x-121) which is not a polynomial because the last term has the variable being raised to a negative exponent because 1/(x-121) = (x-121)^-1.


(x^2 - 6x + 9) / (x-3) results in (x-3) which is a polynomial because the exponent of the variable is a non-negative integer.


looks like the first one and the third one are counter examples because the result of those operations is not a polynomial.


here's some examples of expressions that are polynomial and expressions that are not polynomial.


<a href = "http://www.mathwarehouse.com/algebra/polynomial/polynomial-equation.php" target = "_blank">http://www.mathwarehouse.com/algebra/polynomial/polynomial-equation.php</a>