# How do you do long division of polynomials with remainders?

Dec 24, 2014

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 $3 x + 1$

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

dividend = divisor $\cdot$ quotient + remainder