SOLUTION: Find all zeros of the polynomial P(x)=x^3−x. Its zeros are ___,____ , and ___? Note: if a root has multiplicity more than one, you have to list that root the same

Algebra ->  Finance -> SOLUTION: Find all zeros of the polynomial P(x)=x^3−x. Its zeros are ___,____ , and ___? Note: if a root has multiplicity more than one, you have to list that root the same       Log On


   

Question 1000462: Find all zeros of the polynomial
P(x)=x^3−x.
Its zeros are ___,____ , and ___?

Note: if a root has multiplicity more than one, you have to list that root the same number of times as its multiplicity (this doesn't happen for too many students).
Hint: find one zero (e.g. rational zero theorem and test small values first), then use synthetic division to factor it out. Then you have a quadratic, factor it or maybe use quadratic formula.
Now enter the original polynomial in factored form:

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can factor.
P%28x%29=x%5E3-x
P%28x%29=x%28x%5E2-1%29
P%28x%29=x%28x-1%29%28x%2B1%29
So the zeros are x=0,x=-1,and x=1.