Can you please create a polynomial equivalent to this expression ifn(not \: equal \: sign) - 1\frac{3 + n - 2 {n}^(2) }{1 + n}

Question

can you please create a polynomial equivalent to this expression if
`n(not \: equal \: sign) - 1`
`\frac{3 + n - 2 {n}^(2) }{1 + n}`

Answer 1

Our polynomial is

`(3+n-2n^2)/(n+1),n\\e-1`

This kind of polynomial is actually special, because create polynomials equivalent to it is very simple. For instance, the simplest equivalent polynomial we can create is generated by multiplying and dividing by "n". Doing that gives us

`(3+n-2n^2)/(n+1)\cdot(n)/(n)`
`((3+n-2n^2)n)/((n+1)n)`
`(3n+n\cdot n-(2n^2)n)/((n+1)n)`
`(3n+n^2-2n^3)/(n\cdot n+n)`

`(3n+n^2-2n^3)/(n^2+n),n\\e-1`