Verified answer

(1/5)y^4 + (-3/5)y^2 + (8/5)y

_____________

5y | y^5-3y^3+8y^2

- y^5

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-3y^3+8y^2

- -3y^3

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8y^2

- 8y^2

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0

Divide each term by 5y to get

( y^5 - 3y^3 + 8y^2 ) / 5y = (y^4 -3y^2 + 8y) / 5

Then, factor out the y to get

y(y^3 - 3y^2 + 8) / 5

[(y^4)/5] - [(3y^2)/5] + [8y/5]

i just used parentheses and brackets to make it look more managable

read: "Y to the fourth divided by five, minus three Y squared divided by five, plus eight Y divided by five"