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1)synthetic division

2)polynomial long division method

A)eg.,

divide (x^3)-3(x^2)+3x-1 by (x-1):

1)1 -3 3 -1

(+)

0 1 -2 1

1 -2 1 0---R

here,division is done by adding and multiplying simultaneously i.e.,[1+0=1,1*1=1,-3+1=-2,1*-2=-2,3+(-2)=1,1*1=1,-1+1=0]........n the remainder here is zero...

therefore,[(x^3)-3(x^2)+3x-1]/(x-1)=(x^2)-2x+1

this is synthetic division method......

B)eg.,

divide (x^2)+2x+1 by (x+1)

x+1)x^2+2x+1(x+1

-x^2-(x)

x+1

-x-(1)

0-----remainder

here,first x^2 is divided by x then writing x^2/x=x in quotient.multiply (x+1) with x and write the remainder.again divide came remainder by x.and add it to the quotient.multiply the added one and (x+1).we get remainder as 0.

therefore,(x^2+2x+1)/(x+1)=x+1

this is polynomial long division method.

i hope this will help u.......