SOLUTION: Find all rational zeros of the polynomial {{{p(x)= x^4-2x^3-8x^2+18x-9}}}

Question 306482: Find all rational zeros of the polynomial
Answer by ichudov(507) (Show Source): You can put this solution on YOUR website!
This looks so complicated and intimidating, that the first instinct is to give up.
The second thought that you should always have is that such problems always have simple, easy solutions that school students can easily figure out.
What you know is that if the roots are integer, then the constant part 9, is their product. About the only thing that 9 is divisible by, is 3 and 1. Simple substitution reveals that both 3 and 1 are indeed roots of this polynomial.
Divide the polynomial by (x-1) and then by (x-1) and you get a simple quadratic equation, which you can easily solve. Give it a try.
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