let f(x)=x^3-8x^2+17x-9. Use the factor theorem to find other solutions to f(x)-f(1)=0, besides x=1?

Answer 1

g(x)=f(x)-f(1)=x^3-8x^2+17x-10
here the x(when g(x)=0) is the solution

10=2*5

r(1)=0 OK
r(-1)=-36!=0 NOT
r(2)=0 OK
r(-2)=-84 NOT
r(5)=0 OK
r(-5)=-210 NOT

solution {1,2,5}

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Answer 2

x=2,x=5

Answer 3

f(1)!=0, f(1)=1