Question

Charlie subtracts two polynomials, 5x^2 – 9x^2, and says that the difference proves that polynomials are not closed under subtraction.Kate argues that the difference does in fact show that polynomials are closed under subtraction. Who is correct? Type only 'Charlie' orKate' as your answer in the box.

Answer 1

Charlie

Here, we want to check if polynomials is closed under subtraction or not

To check this, we proceed either ways, if the answer is same, then it is closed. If otherwise, then it is not

We have;

`\begin{gathered} 5x^2-9x^2=-4x^2 \\ \\ \text{And;} \\ \\ 9x^2-5x^2=4x^2 \end{gathered}`

As we can see, both results are not equal

If subtraction was closed under polynomials, then the results of both should have been equal. This means Charlie is correct.