Answer: The quotient is 3y² + 2y - 1.
Explanation:
You can use long division to solve this expression by setting the dividend under the roof and the divisor outside as you would normally do when dividing numbers.
1) Look at the first term of the dividend, 15y³, and the first term of the divisor, 5y. Determine what value multiplied by 5y would give you 15y³. The answer is 3y², and given the number, you multiply it by the WHOLE divisor.
3y²(5y + 6) = 15y³ + 18y² <-- subtract this from the dividend.
2) Continue this process and make sure to drag down the next term for each new value you form after subtracting. Keep in mind of any negative values! When you reach up to -5y, determine what value multiplied by 5y would give you the value of -5y, which would be -1.
3) You should be left with a remainder of 0, leaving you with a quotient of 3y² + 2y - 1.