SOLUTION: Solving higher polynomials, remainder, factor and rational root theorems: Determine the points of intersection of {{{y=x^3-1}}} and {{{y=-x^2 -2x -1}}} I know from graphing t

Question 864306: Solving higher polynomials, remainder, factor and rational root theorems:
Determine the points of intersection of
and
I know from graphing that there is one point of intersection but how do I determine it using remainder, factor and rational root theorems? I've tried but keep getting the wrong answer.

Thanks
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
y=x^3-1 and y=-x^2 -2x -1
set them equal and solve for x then plug in your x and find y
x^3-1 =-x^2 -2x -1
x^3-1+x^2 +2x +1=0
x^3+x^2+2x =0
the constant=0 therefore the factor is 0
factor out x
x=0 plug in 0 and find y=-1
one real solution
x = 0, y = -1
x^2+x +2=0
solve for the two complex solutions

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