Division of polynomials

To divide monomials, we divide the coefficients and the literal parts.

To divide polynomials first, we divide the higher degree monomial of the dividend by the higher degree monomial of the divisor and put the resulting monomial in the quotient. Then, we multiply this monomial by the divisor and subtract from the dividend, obtaining a new dividend in the remainder, and we go on until we reach a remainder whose degree is lower than the divisor one.

  Dividend = divisor · quotient + remainder

Exercise: divide:

a) (x⁵-3x⁴-x³+13x²-17x+19):(x³-3x+4)

b) (x⁷-5x⁴+x³+2x²-24x-8):(x⁴+3x+1)

Solutions: a) quotient = x²-3x+2, remainder = x+11; b) quotient = x³-8; remainder = 2x²