Without actual division, prove that `x^4+2x^3-2x^2+2x-3` is exactly divisible by `x^2+2x-3.`

Explanation

Let, `p(x)=x^4 +2x^3 −2x^2+x−1`
`g(x)=x^2 +2x−3`
From the above division of polynomial `p(x)` by `g(x)` we can conclude that the remainder is `−x+2`.
So, if we add negative of this to the polynomial `p(x)` then `g(x)` will divide `p(x)` completely.
`−(−x+2)=x−2`
So, `x−2` should be added to the polynomial `p(x)`.