Question

Which operation is NOT closed for polynomials?

Answer 1

#1

`\\ \sf\longmapsto x^3+4x^2+2x-5+x^2+3x+1`

`\\ \sf\longmapsto x^3+5x^2+5x-4`

• Polynomial ✓

#2

`\\ \sf\longmapsto x^3+4x^2+2x-5-x^2-3x-1`

`\\ \sf\longmapsto x^3+3x^2-x-6`

• Polynomial✓

#3

`\\ \sf\longmapsto x^3+4x^2+2x-5(x^2+3x+1)`

• Polynomial✓

#4

Option D may not be a polynomial

Answer 2

• Option D

Explanation:

When you add, multiply or subtract polynomials, the operation results in another polynomial.

When dividing polynomials, the operation may not result in another polynomial. In this case you normally end up with rational expression in the fraction form.

This operation is said not closed.

In our case this is option D.