SOLUTION: one factor of x^3 + 1 is (x + 1). what is the other factor ?

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Question 322027: one factor of x^3 + 1 is (x + 1). what is the other factor ?
Found 2 solutions by nyc_function, Jk22:
Answer by nyc_function(2741) About Me  (Show Source):
You can put this solution on YOUR website!
Use the sum of cubes formula.
A^3 + B^3 = (A + B)(A^2 - AB + B^2)
x^3 + 1 = x^3 + 1^3
Let A = x
Let B = 1
x^3 + 1 = (x + 1)(x^2 - (x)(1) + 1^2)
x^3 + 1 = (x + 1)(x^2 - x + 1)
The other factor is (x^2 - x + 1).

Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
dividing x^3+1 by x+1 gives :
x^3+1....|x+1
_____________
x^3+x^2..|x^2
_________
-x^2+1...|-x
-x^2-x...|
_________
x+1......| 1
x+1......|
_________
0
=> (x^3+1)/(x+1)=x^2-x+1