Factor $x^2+5xy+6y^2+x+3y$ as the product of two polynomials of degree 1.

Factor:  x² + 5xy + 6y² + x + 3y

Factoring the first three terms:

--->       (x + 3y)(x + 2y) + x + 3y

--->       (x + 3y)(x + 2y) + (x + 3y)

--->       (x + 3y)(x + 2y) + (x + 3y)(1)

--->       (x + 3y)(x + 2y) + (x + 3y)(1)

Factoring out the common term of x + 3y:

--->       (x + 3y) [ (x + 2y) + 1 ]

--->       (x + 3y)(x + 2y + 1)