SOLUTION: Let f(x)=-x^3+3x^2-3x+1, and g(x) be f(x) divided by 1-x; solve for g(x) if 1-x is a factor of f(x). a. g(x)=x^4-4x^3+6x^2-4x+1 b. g(x)=x^3-3x^2+3x-1 c. g(x)=-x^2+2x-1 d. g

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Question 154518: Let f(x)=-x^3+3x^2-3x+1, and g(x) be f(x) divided by 1-x; solve for g(x) if 1-x is a factor of f(x).
a. g(x)=x^4-4x^3+6x^2-4x+1
b. g(x)=x^3-3x^2+3x-1
c. g(x)=-x^2+2x-1
d. g(x)=x^2-2x+1
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
Let , and be divided by ; solve for if is a factor of .
a.
b.
c.
d. 

Let's first factor : 

 

Regroup the terms:

,

Factor the first two terms as the difference of cubes:
Factor out  out of the last two terms:



Factor out 

 

Remove the inner parentheses:



Combine the two like terms:



Factor the second parentheses:



Write as a cube:



Now since

g(x) is f(x) divided by 1-x



So the correct choice is (d)

Edwin
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