How to use synthetic division to show how to methodically obtain the factors from the polynomial 2x^5+6x^4-42x^3-86x^2+192x+360

Okay so first you need to find your prrs which in this case would be all factors of 360 and all of the factors of 360 divided by two since the factors of two are two and one. (Which I pulled from the first x’s coefficient)

Then you do Descartes law to find out how many positives or negatives in this equation. There looks to be 2 positives and 3 or 0 negatives. Since there are guaranteed positives I’d recommend doing those first. Start from the lowest number since that’s easier and more mathematically correct and do synthetic division. (x+1) The resulting polynomial should be factorable and of not then try to synthetically divide again.

The answer to that is 6