Roughly, to divide a polynomial by a monomial; you have to divide each part of the polynomial by the monomial.
For example, for (2x2 + 4x) ÷ 2x; we do 2x2 ÷ 2x = x and then 4x ÷ 2x = 2. All together, we get x + 2.
Here's another example, (24x5 + 9x3 - 6x2) ÷ 3x2 can be solved by doing 24x5 ÷ 3x2 = 8x3, 9x3 ÷ 3x2 = 3x, and 6x2 ÷ 3x2 = 2. All together, we have 8x3 + 3x - 2. Our answer has the same addition and subtraction signs because they don't change when we divide.