Find the remainder if the polynomial f(x) = 3x^100 + 5x^87 - 4x^40 + 2x^21 - 6 divided by p(x) = x + 1
The thing is, I can't use synthetic OR long division BECAUSE I'd have a VERY VERY long equation (since you have to fill in the missing degrees: 99,98,97,96,95......etc).
How would you solve this?
you should use it at this way:
so let's say that:
and is the unknown answer
so rewriting the cocient and according to the remainder theorem:
where r(x) is the remainder
knowing the remainder then use synthetic division to do the operation which is easier to do.