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f(x) =x^4-2x^3+2x-1
f(1) =0
x^4-2x^3+2x-1 =(x-1)(x^3+ax^2+bx +1)
coef. of x
1-b=2
b=-1
coef. of x^2
b-a=-2
-1-a=-2
a=1
x^4-2x^3+2x-1 =(x-1)(x^3+x^2-x +1)
h(x) =x^3+x^2-x +1
h(1)=0
x^3+x^2-x +1 =(x-1)(x^2+cx-1)
coef. of x
-1-c=-1
c=0
x^3+x^2-x +1 =(x-1)(x^2-1) =(x-1)^2.(x+1)
ie
x^4-2x^3+2x-1
=(x-1)(x^3+x^2-x +1)
=(x-1)^3.(x+1)
g'(x)
= 3x^2 -6x+6/x -3/x^2
=(3x^4-6x^3+6x-3)/x^2
=3(x^4-2x^3+2x-1)/x^2
=3(x-1)^3.(x+1)/x^2
f(1) =0
x^4-2x^3+2x-1 =(x-1)(x^3+ax^2+bx +1)
coef. of x
1-b=2
b=-1
coef. of x^2
b-a=-2
-1-a=-2
a=1
x^4-2x^3+2x-1 =(x-1)(x^3+x^2-x +1)
h(x) =x^3+x^2-x +1
h(1)=0
x^3+x^2-x +1 =(x-1)(x^2+cx-1)
coef. of x
-1-c=-1
c=0
x^3+x^2-x +1 =(x-1)(x^2-1) =(x-1)^2.(x+1)
ie
x^4-2x^3+2x-1
=(x-1)(x^3+x^2-x +1)
=(x-1)^3.(x+1)
g'(x)
= 3x^2 -6x+6/x -3/x^2
=(3x^4-6x^3+6x-3)/x^2
=3(x^4-2x^3+2x-1)/x^2
=3(x-1)^3.(x+1)/x^2
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