Divide. If the polynomial does not divide evenly, include the remainder as a fraction.
(5q^5 - 25q^4 + 29q^3 + 9q) ÷ (q - 3)

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Divide. If the polynomial does not divide evenly, include the remainder as a fraction. (5q^5 - 25q^4 + 29q^3 + 9q) ÷ (q - 3)

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To divide the polynomial (5q^5 - 25q^4 + 29q^3 + 9q) by (q - 3), we use polynomial long division: Divide the first term of the dividend by the first term of the divisor: 5q^5 ÷ q = 5q^4. Multiply the entire divisor by this result: 5q^4(q - 3) = 5q^5 - 15q^4. Subtract this from the original polynomial: (5q^5 - 25q^4) - (5q^5 - 15q^4) = -10q^4. Bring down the next term: -10q^4 + 29q^3. Repeat the process: -10q^4 ÷ q = -10q^3. Multiply and subtract: -10q^3(q - 3) = -10q^4 + 30q^3, so (-10q^4 + 29q^3) - (-10q^4 + 30q^3) = -q^3. Bring down the next term: -q^3 + 9q. Repeat: -q^3 ÷ q = -q^2. Multiply and subtract: -q^2(q - 3) = -q^3 + 3q^2, so (-q^3 + 9q) - (-q^3 + 3q^2) = -3q^2 + 9q. Repeat: -3q^2 ÷ q = -3q. Multiply and subtract: -3q(q - 3) = -3q^2 + 9q, so (-3q^2 + 9q) - (-3q^2 + 9q) = 0. The quotient is 5q^4 - 10q^3 - q^2 - 3q with no remainder.

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Divide. If the polynomial does not divide evenly, include the remainder as a fraction. (5q^5 - 25q^4 +...

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