Question 426945
{{{ x^4-2x^3-7x^2+18x-18
= x^4-2x^3 + 2x^2 - 9x^2+18x-18

= x^2(x^2 - 2x + 2) - 9(x^2 - 2x + 2)
= (x^2 - 9)(x^2 - 2x + 2)}}}
{{{x^2 - 2x + 2}}} has no real zeroes ( the discriminant is -4).

The only zeroes are x = 3,-3.








NOTES TO THE TUTOR BELOW:

1) You are wrong in saying that a polynomial is not a rational function.  It is, because the denominator of a polynomial is 1, and any constant is considered a polynomial of degree 0.  Know your algebra.
2) You said "And since I don't see how factoring by grouping will work, we seem to be left with just factoring by trial and error of the possible rational roots."  If you cared to read my solution, I HAVE FACTORED THE POLYNOMIAL BY GROUPING.  BTW, it's called Rational Zeros Theorem.