Expert: Paul Klarreich - 7/8/2009

Question
Use descartes rule of signs and the rational zeros theorom to find all the real zeros, then use the zeros to factor over the real numbers.

f(x)= x^4+6x^3+11x^2+12x+18

I have it all worked out, but i am stuck at the depressing equation. I got
4 real zeros
Descartes: no positive real zeros
          4 negative real zeros
rational zeros: -3 is a zero of f. so (x+3)can be factored out and usig long division. i got (x+3)(x^3+3x^2+2x+6). im stuck here, what do i do next ? i cannot factor it, if i do long divison using x-3 it doesnt work out. Please help

Answer
Why did you not try  -3?  Yes, I know you tried it and it worked for your first division, but it could still be a root of the depressed equation.  So you should try it again.  It could be a double root and that would certainly cure your depressed state.  (Sorry!)