Polynomial division is an important mathematical tool and an essential part of solving more complex equations. In this article, we will break down the process of dividing polynomials into 10 simple steps. Before we start, make sure you are familiar with polynomial terms and degrees.

1. Identify the dividend and divisor: The dividend is the polynomial that is being divided, while the divisor is the polynomial you are dividing by.
2. Arrange the dividend and divisor in descending order of their exponents.
3. Compare the leading term of the dividend (highest degree term) with the leading term of the divisor.
4. Calculate the ratio between the leading terms of both polynomials, by dividing the coefficient of the dividend’s leading term by that of the divisor’s leading term.
5. Multiply all terms in the divisor polynomial with this ratio.
6. Align this new polynomial (from step 5) with divisor in such a way that their leading terms are aligned vertically.
7. Subtract this new polynomial from divisor to obtain a polynomial remainder.
8. Repeat steps 3-7 with this new remainder until a lower-degree remainder is achieved or until no more terms in the dividend can be divided by any term in the divisor.
9. Write down your quotient as a sum/difference of all previously calculated ratios.
10. Combine any like terms in your final quotient and simplify if needed.

Now you have successfully divided polynomials! Keep practicing to improve your skills, and soon you’ll be able to divide polynomials with ease. Remember, as long as you follow these 10 steps carefully, you’ll be well on your way to mastering polynomial division!