Mathematics NaeNae:

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

5 months ago tetheredrain:

Do you have the equations? Your question is missing the equations.

5 months ago NaeNae:

Multiplication: (x^2-5x+3)(x-5)=x^3-10x^2+28x-15 Division: (x^2-5x+3) / (x-5)=x+ 3/x-5 Division: (x^2+x)/(x+1)=x Subtraction: (3x^4 +x^3)-(-2x^4+x^3)=5x

5 months ago tetheredrain:

The best answer is "Division: (x^2-5x+3) / (x-5)=x+ 3/x-5" Note that $$(x+3)/(x-5)$$ is not a polynomial. Basically, a set is "closed" under an operation if you do that operation with members of the set and you still get a result that is still in the set. A polynomial is an algebraic expression with variables and terms; the only operations in a polynomial should be addition, subtraction, multiplication. All variables should have nonnegative integer exponents, i.e. {0,1,2,3,...}. So things such as $$x^2 + 3x + 4$$ and $$1 (=x^0)$$ and $$3x^2y+5y$$ are polynomials but $\frac{x^2+3}{4-x}$ is not a polynomial because there is division. So you can see in that example, doing division got you something that is not a polynomial

5 months ago
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