how to factor $x^4+2x^3+4x^2+3x+2$ I'm trying my hand on these types of expressions.
How to factorize $x^4+2x^3+4x^2+3x+2$ into two  (or more) polynomials with rational coefficients.  please write step by step solution.

I think the best way is by intuition.
$x^4+2x^3+4x^2+3x+2$
$=(x^4+x^3+x^2)+(x^3+x^2+x)+(2x^2+2x+2)$
$=x^2(x^2+x+1)+x(x^2+x+1)+2(x^2+x+1)$
$=(x^2+x+1)(x^2+x+2)$
