Do you expect polynomials to be closed under division? Explain.
A. No. For example, (x^2 + 2)/x = x + 2/x which is not a polynomial.
B. No. For example, (x + x^2)/x = 1 + x, which is not a polynomial.
C. Yes. The quotient of any two polynomials is always a polynomial.
D. Yes. The quotient of any two polynomials is sometimes a monomial.
A. No. For example, (x^2 + 2)/x = x + 2/x which is not a polynomial.
Polynomials are algebraic expressions consisting of variables, coefficients, and exponents, combined using operations of addition, subtraction, and multiplication. Division of polynomials may result in expressions that are not considered polynomials, as shown in the given example. Therefore, we do not expect polynomials to be closed under division.