I've read that we can divide any polynomial by a linear polynomial by synthetic division considerably faster than that by long division method.
Now, I've learnt the steps to do so but I don't quite understand how it works.
Because here rather than dividing by the factor we are dividing by the zero ( i.e.* root*) and apparently these two cases are quite different.
But, in a way, the steps involved in this method seem to be equivalent to that in the long division but I haven't been to fully grasp how and why that is so.
Bonus Question:- Also, is there a similar relatively easy method for dividing by higher degrees polynomials too?