Factor 10x^4+55x^3y+6xy+33y^2

$10 x^{4} + 55 x^{3} y + 6 x y + 33 y^{2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(10 x^{4} + 55 x^{3} y) + 6 x y + 33 y^{2}$

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

$5 x^{3} (2 x + 11 y) + 3 y (2 x + 11 y)$

Factor the polynomial by factoring out the greatest common factor, $2 x + 11 y$ .

$(2 x + 11 y) (5 x^{3} + 3 y)$