I seem to have encountered a situation in which I have a quartic which has solutions, but no factors. The polynomial is: [itex]x^4 - 8x^2 + 224x - 160 = 0[/itex] I attempted to find the factors for this quartic in the following manor [itex]f(x) = x^4 - 8x^2 + 224x - 160[/itex] [itex]f(1) = (1)^4 - 8(1)^2 + 224(1) - 160[/itex] [itex]f(1) = 60[/itex] [itex]f(2) = (2)^4 - 8(2)^2 + 224(2) - 160[/itex] [itex]f(2) = 272[/itex] [itex]...[/itex] [itex]f(8) = (8)^4 - 8(8)^2 + 224(8) - 160[/itex] [itex]f(8) = 5216[/itex] So basically, after I got 8 (negative versions included) I gave up on this method and decided to attempt to factorise it on my calculator. However, my calculator refuses to break down this equation into it's respective equations. However, when I solve the equation it gives me two, real answers: [itex]x = -6.705505492, x = 0.7321472234[/itex]. Also, the calculator refuses to give these answers in standard form, only decimal form. Normally when I solve an equation in standard form, it gives me the answer in fractional, surd, or even trigonometrical form. This is really confusing me, so if anyone could explain to me how it is possible for an equation to have real answers, yet it can't be factorised?