\( x ^ { r } + r x ^ { r } + r x - r = \)

To factor the expression \( x^{r} + r x^{r} + r x - r \), we can group some of the terms. Notice that we can factor out \( x^{r} \) from the first two terms and factor out \( r \) from the last two terms: \[ x^{r} (1 + r) + r(x - 1) \] This gives us a more manageable form. Depending on the context for which you need the information, you can simplify or analyze this further. It’s also interesting to note how polynomial terms can be manipulated; there's a blend of creativity and algebra here! Consider how changing the values of \( r \) can entirely alter the shape of this polynomial, adding a layer of complexity to your problem-solving journey. Keep experimenting!