Question

which of the following equations demonstrate that the set of polynomials is not closed under the certain operations? A. Division: (x^2+2x) / (x+1) = x+ x/x+1 B. Multip.: (3x^4+x^3)(-2x^4+x^3)= -6x^6+ x^7+x^6 C. Addition: (3x^4+x^3)+(-2x^4+x^3)= x^4 + 2x^3 D. Multip.: (x^2+2x)(x+1)= x^3 +3x^2+2x

Answer 1

Division: (x^2+2x) / (x+1) = x+ x/x+1

Step-by-step explanation:

Answer 2

The correct answer is A) Division.

Step-by-step explanation:
When we divide these two polynomials, we get an answer that is not a polynomial. This is due to the rational portion of the answer, x/(x+1).

We know from our definitions of polynomials and monomials that if there is a variable with a negative exponent, that means that we do not have a monomial and therefore not a polynomial. Having x+1 in the denominator means it would have a negative exponent, and is therefore not a polynomial.

Since we divided two polynomials and had a result that was not a polynomial, this means that the set of polynomials is not closed under division.