SOLUTION: f(x)=x^6-x^5-x^4+x^3 find all the zeros and the multiplicity of each zero.

Question 690480: f(x)=x^6-x^5-x^4+x^3
find all the zeros and the multiplicity of each zero.

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
f(x)=x^6-x^5-x^4+x^3
find all the zeros and the multiplicity of each zero.
.
x^6-x^5-x^4+x^3
x^3(x^3-x^2-x+1)
now, we find roots of polynomial within parentheses...try a 1 first using synthetic division:
1 1 -1 -1 1
1 0 -1
-------------
1 0 -1 0
now, we have
x^3(x-1)(x^2-1)
difference of squares:
x^3(x-1)(x-1)(x+1)
x^3(x-1)^2(x+1)
.
Zeros are:
x=0 with multiplicity of 3
x=1 with multiplicity of 2
x=-1 with multiplicity of 1

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