1. By a monomial

E.g.; Divide the polynomial p(x) by the monomial 2x, where,

p(x) = 2x³ + 4x² - 5x – 1

Solution

p(x)2x=2x3+4x2-5x-12x=2x32x+4x22x+-5x2x+-12x=x2+2x-52-12x

2. By another polynomial

This division is often done by the long division method.

Example; the polynomial p(x) is given by, p(x) = 2x³+3x²-4x-20, find; p(x) ÷ (x – 2)

Solution                               

             2x²+7x+10

X - 2/2x³+3x²-4x-20

• (2x³ – 4x²)    

            7x² – 4x

•  (7x² – 14x)

           10x – 20

•       (10x – 20)

        _        _

∴ p(x) ÷ (x – 2) =  2x²+7x+10