Factoring $x^4-2x^3+2x^2+x+4$ 
I need to show that the polynomial is not irreducible and I am trying to factor the polynomial 
  $$x^4-2x^3+2x^2+x+4$$

I checked from a calculator that it has a factor but how do I get it by myself?
I tried grouping but It didnt work I got 
$x^2(x^2-2x+2)+x+4$ And I dont know how should I proceed. My guts tell me that it should be of the form:
$(x^2-ax+k)(x^2+bx+l)$, should I just try to figure out the constants by trying out?

Use the Rational Root Test to check if there is any real roots. It turns out that there is no such roots of this polynomial. Hence, the conclusion is that there can only be complex roots. By the fundamental theorem of Algebra, we know any non constant single variable polynomial has at least one complex root (including real ones). 
As you have mentioned, assume that the polynomial is the product of two quadratic polynomials. Solve them and find constants $a,b,k$ & $l$
