Factoring a given polynomial may in certain special cases succeed by using the following grouping method:

1. Group the terms of the polynomial in two (or sometimes more) suitable groups.
2. Factorize the groups separately.
3. The whole polynomial may then possibly be written in form of a product.

Examples

a) $x^3-x^2-x+1 = \{x^3-x^2\}+\{-x+1\} = x^2(x-1)-1(x-1) = (x-1)(x^2-1)\\ = (x-1)^2(x+1)$

b) $x^4+3x^3-3x-1 = \{x^4-1\}+\{3x^3-3x\} = (x^2+1)(x^2-1)+3x(x^2-1)\\ = (x^2-1)(x^2+1+3x) = (x-1)(x+1)(x^2+3x+1)$

c) $x^4+4 = \{x^4+4x^2+4\}-4x^2 = (x^2+2)^2-(2x)^2 = (x^2+2+2x)(x^2+2-2x)\\ = (x^2+2x+2)(x^2-2x+2)$

d) $x^4+x^2+1 = \{x^4+2x^2+1\}-x^2 = (x^2+1)^2-x^2 = (x^2+1+x)(x^2+1-x)\\ = (x^2+x+1)(x^2-x+1)$

The trinomials $x^2\!+\!3x\!+\!1$ , $x^2\!\pm\!2x\!+\!2$ and $x^2\!\pm\!x\!+\!1$ are irreducible polynomials.