How do you list all possible rational roots for each equation, use synthetic division to find the actual rational root, then find the remaining 2 roots for #x^3-2x^2+9x-18=0#?

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Answer 1 · 2016-07-27T01:07:16

The list of possible root are the divisors of 18 :
#+-1 | +-2 |+- 3 | +-6 | +-9 | +-18#

Actually the polynomial given is factored quite easily

#x^3-2x^2+9x-18=0=>x^2(x-2)+9(x-2)=0=> (x-2)*(x^2-9)=0=>(x-2)(x-3)(x+3)=0#

Hence the roots are #2,3,-3#

Using synthetic division we have that

   1 -2 9 -18 | 2
         1   -9  | 0

Hence #(x^3-2x^2+9x-18)=(x-2)*(x^2-9)+0#