Question

Which polynomial is equivalent to this expression if n≠-1n≠-1? 3+n−2n21+n?

Answer 1

Equivalent Polynomial of given polynomial is 3 - 2n.

Explanation:

We are given following polynomial:

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

We have top find equivalent polynomial such that n ≠ -1

Consider,

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

`=(3+3n-2n-2n^2)/(1+n)`

`=(3(1+n)-2n(1+n))/(1+n)`

`=((1+n)(3-2n))/(1+n)`

`=3-2n`

Therefore, Equivalent Polynomial of given polynomial is 3 - 2n.

Answer 2

I suppose that the expression you wanted to write is
`(3+n-2n^2)/(1+n)`. If so, then we have:


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