Question

How do you do long division of polynomials with remainders?

Answer 1

It is the same but just instead of getting 0 you get a polynomial in the last step.

Divide `3x^3 – 5x^2 + 10x – 3` by `3x + 1`

in this case you get a polynomial seven which can be writtten in algebraic terms as `7x^0`
so this can be proved using the division algoritm

dividend = divisor `*` quotient + remainder