Final answer:
To divide (8y^2+17y) by (2y) using long division, divide the highest degree term of the numerator by the denominator. Subtract the product of the divisor and the quotient from the numerator. Repeat the process with the new numerator until the numerator is less than the denominator. The quotient is the sum of the previous quotients.
Step-by-step explanation:
To divide (8y^2+17y) by (2y) using long division, we start by dividing the highest degree term of the numerator by the denominator. In this case, 8y^2 divided by 2y is 4y. We then multiply 4y by the denominator and subtract it from the numerator. This gives us (8y^2+17y) - 4y(2y) = 17y - 4y(2y) = 17y - 8y^2. We repeat the process with the new numerator, bringing down the remaining terms. We divide 17y by 2y, which is 8.5, but since we are looking for whole numbers, we round it down to 8. We then multiply 8 by the denominator and subtract it from the numerator. This gives us (17y - 8y^2) - 8(2y) = -16y - 8(2y) = -16y - 16y = -32y. Since the numerator (-32y) is less than the denominator (2y), we cannot continue dividing and the quotient is 4y + 8 - (32y/2y) = 4y + 8 - 16 = 4y - 8.