Answer: When dividing a polynomial by a monomial, we can simply divide each term in the polynomial by the monomial.
So, dividing (8zy² - 28z¹y5 + 12z³y7) by (4z¹y³) gives:
(8zy²)/(4z¹y³) - (28z¹y5)/(4z¹y³) + (12z³y7)/(4z¹y³)
Simplifying each term by canceling out any common factors gives:
2y^(-1)z^(1-1) - 7y^(5-3)z^(1-1) + 3y^(7-3)z^(3-1)
which simplifies to:
2yz^0 - 7y^2z + 3y^4z^2
Therefore, (8zy² - 28z¹y5 + 12z³y7) ÷ (4z¹y³) = 2yz^0 - 7y^2z + 3y^4z^2.
Explanation: