Factor 2x^2+x+4x+2

$2 x^{2} + x + 4 x + 2$

Reorder terms.

$2 x^{2} + 4 x + x + 2$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} + 4 x) + x + 2$

Factor out the greatest common factor (GCF) from each group.

$2 x (x + 2) + 1 (x + 2)$

Factor the polynomial by factoring out the greatest common factor, $x + 2$ .

$(x + 2) (2 x + 1)$