How do you use polynomial division to determine whether x=3 is a root of #x^3+x^2+15-x#?
If you can divide without a remainder,
If you have a remainder, it's not a root.
Well, just to check if
But of course, it is also possible to determine the outcome with polynomial division.
To do so, you must divide
I know that in some countries, a different notation for long division is being used but I will use the one that I'm familiar with and I hope that it will be no problem for you to rewrite it in your notation if necessary.
At the end of the computation, there is the remainder
As you have a remainder, it means that