SOLUTION: The questions states to find all integral solutions for the polynomial equation: x^4+x^3+x+1 I started out factoring by grouping which gives me x^3(x+1)+(x+1)..but I am tota

Question 44804This question is from textbook functions and change
: The questions states to find all integral solutions for the polynomial equation:
x^4+x^3+x+1
I started out factoring by grouping which gives me x^3(x+1)+(x+1)..but I am totally stumped on what the solutions are.
Thanks in advance for your help
T Taylor This question is from textbook functions and change

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x^4+x^3+x+1
If you substitute x=-1 you get zero.
So -1 is a solution.
Divide by x+1 to get x^3+1
This also has a zero of -1
The remaining factor is x^2-x+1
Use the quadratic formula if you want but
you won't find any other integer solutions.
So the interger solutions are -1 with multiplicity two.
Cheers,
Stan H.

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