Final answer:
To divide the polynomial by 2y, we can use long division. The quotient of 6y^(4) + 10y^(3) - 8y^(2) divided by 2y is 3y^(3) + 5y^(2) - 4y.
Step-by-step explanation:
To divide 6y^(4)+10y^(3)-8y^(2) by 2y, we can use long division.
Starting with the highest exponent, divide 6y^(4) by 2y to get 3y^(3). Multiply 3y^(3) by 2y to get 6y^(4). Subtract 6y^(4) from the original polynomial to get 0.
Next, divide 10y^(3) by 2y to get 5y^(2). Multiply 5y^(2) by 2y to get 10y^(3). Subtract 10y^(3) from the remaining polynomial to get 0.
Finally, divide -8y^(2) by 2y to get -4y. Multiply -4y by 2y to get -8y^(2). Subtract -8y^(2) from the remaining polynomial to get 0.
Therefore, the quotient of 6y^(4)+10y^(3)-8y^(2) divided by 2y is 3y^(3) + 5y^(2) - 4y.