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Anna Greer Polynomial Divided by Monomial Mar 15, 8:48:19 AM Find the quotient of (40y)⁴-(5y)³-(30y) ²-10y divided by 5y

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Final answer:

To divide the polynomial (40y)⁴-(5y)³-(30y)²-10y by the monomial 5y, use polynomial long division. The quotient is 8y³ - y² - 6y - 2.

Step-by-step explanation:

To divide the polynomial (40y)⁴-(5y)³-(30y)²-10y by the monomial 5y, you need to use polynomial long division.

Step 1: Divide the first term of the polynomial by the monomial.

(40y)⁴ ÷ 5y = 8y³

Step 2: Multiply the monomial by the result from Step 1, and subtract it from the original polynomial.

(40y)⁴ - (8y³ * 5y) = (40y)⁴ - 40y⁴ = 0

Step 3: Repeat Steps 1 and 2 with the remaining terms of the polynomial.

(-5y)³ ÷ 5y = -y²

(-5y)³ - (-y² * 5y) = (-5y)³ + 5y³ = 0

(-30y)² ÷ 5y = -6y

(-30y)² - (-6y * 5y) = (-30y)² + 30y² = 0

(-10y) ÷ 5y = -2

(-10y) - (-2 * 5y) = (-10y) + 10y = 0

Step 4: The final quotient is the sum of the quotients obtained in each step.

Final quotient: 8y³ - y² - 6y - 2

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