Question

Which of the following equations demonstrate that the set of polynomials isnot closed under the certain operations?A. Multiplication: (x2 + 2x)(x + 1) = x + 3x2 + 2xхB. Division: (x2 + 2x) = (x + 1) = x+x +1C. Addition: (3 x4 + x°)+(-2x4 + x) = x4 + 2x3+D. Multiplication: (3x4 + **)(-2x4 + x) = -6x + x + x

Answer 1

Verify each equation

A

`(x^2+2x)(x+1)`

Applying distributive property

`\begin{gathered} (x^2+2x)(x+1)=x^3+x^2+2x^2+2x \\ x^3+3x^2+2x \end{gathered}`

A is not the answer

B

we have