1. The problem statement, all variables and given/known data Let [itex]x\in[/itex]R, Prove that if x>2 then [itex]x^4 - 8x^3+24x^2-32x+16[/itex] 2. Relevant equations 3. The attempt at a solution So far I have only learned proofs involving even and odd numbers, that sort of thing. I'm not really sure how to approach this one. I was thinking that a proof by cases would suffice, so: Proof: Case I: Assume that x>2, and let S = (0,[itex]\infty[/itex]). If follows that, x = (m+2) for some m[itex]\in[/itex]S. And so, [itex]x^4 - 8x^3+24x^2-32x+16 = (m+2)^4 - 8(m+2)^3+24(m+2)^2-32(m+2)+16[/itex] but now I see the problem becoming too difficult. We haven't learned about epsilon-delta et al. yet. I can see that the conclusion is ALWAYS true, so really the proof is trivial, but I am not sure how to say that.