Factor the given polynomial by finding the greatest common monomial factor (or the negative of the \[ -22 y-22 x+22 x^{2} \]

To factor the polynomial \(-22y - 22x + 22x^2\), we first look for the greatest common factor (GCF) of the terms. Here, the GCF is \(-22\), as it can be factored out of each term. Factoring gives us: \[-22(y + x - x^2).\] Next, we can rearrange the terms inside the parentheses for clarity: \[-22(-x^2 + x + y).\] This reveals that the polynomial can be expressed simply as: \[-22(x^2 - x - y).\] So the factored form of the polynomial is \(-22(x^2 - x - y)\). Now you've got a nice, neat format to work with!