Question

Which of the following equations demonstrate that the set of polynomials is

not closed under the certain operations?
A. Subtraction: (3x^4+x^3)-(-2x^4+x^3)=5x^4
B. Addition: (x^2+x)+(x+1)=x^2+2x+1
C. Division: (x^2-5x+3)÷(x-2)=x-3+-3/x-2
D. Multiplication: (x^2-5x+3)(x-5)=x^3-10x^2+28x-15

Answer 1

9514 1404 393

Answer:

C. Division: (x^2-5x+3)÷(x-2)=x-3+-3/x-2

Explanation:

The set of polynomials is closed under all basic arithmetic operations except division. The reciprocal of a (non-constant) polynomial is not a polynomial.

The division example shown in choice C illustrates the set is not closed under division.