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foreign hello guys welcome back PK here so Im looking at this interesting algebra question the basic quintic equation that you can see the question is solved for all the solutions for the equation x to the power of 5 minus 1 is equal to zero so for this question we will be using this famous formula to factor this left-hand side out that was x to the power of n minus 1. we can Factor this out as x minus 1 times x to the power of n minus 1 plus x to the power of n minus two plus all the way up to one we will be using this formula directly to factor this left-hand side out right okay then the left hand side is now going to be equal to x minus 1 times x to the power of 4 plus X cubed plus x squared plus X Plus now one this is equal to zero based on the question so by taking a look at this factor of the form then we can get one solution quite easily that should be X is equal to one right so that is case number one heres number one your x minus one is equal to zero which means that X is e