Question

Which of the following equations demonstrate that the set of polynomials is not closed under the certain operations?

A. Subtraction: (3x4 + x) - (-2x4 + x) = 5x4
B. Multiplication: (x2 - 5x+3)(x - 5) = x3 - 10x2 +28x - 15
C. Division: (x2+x)=(x + 1) =X
D. Division: (x2 - 5x + 3) + (x-5) = x + -3/X-5

Answer 1

D. Division: (x² - 5x + 3) ÷ (x-5) = x + 3/(x - 5)

Explanation:

Polynomials are closed under subtraction and multiplication because any subtraction or multiplication of polynomials gives as result another polynomial.

As can be seen in option D, polynomials aren't closed under division because not every division between polynomials gives as result another polynomial.