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Divide. If there is a remainder, include it as a simplified fraction.\newline(5m336m281m)÷(m9)(5m^3 - 36m^2 - 81m) \div (m - 9)\newline______

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Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(5m336m281m)÷(m9)(5m^3 - 36m^2 - 81m) \div (m - 9)\newline______
  1. Divide by First Term: We will use polynomial long division to divide (5m336m281m)(5m^3 - 36m^2 - 81m) by (m9)(m - 9). First, we divide the first term of the dividend, 5m35m^3, by the first term of the divisor, mm, to get the first term of the quotient. 5m3÷m=5m25m^3 \div m = 5m^2
  2. Subtract and Multiply: Now, we multiply the entire divisor (m9)(m - 9) by the first term of the quotient (5m2)(5m^2) and subtract the result from the dividend.\newline(5m2)(m9)=5m345m2(5m^2) \cdot (m - 9) = 5m^3 - 45m^2\newlineSubtract this from the dividend:\newline(5m336m281m)(5m345m2)=9m281m(5m^3 - 36m^2 - 81m) - (5m^3 - 45m^2) = 9m^2 - 81m
  3. Divide New Term: Next, we divide the first term of the new dividend, 9m29m^2, by the first term of the divisor, mm, to get the next term of the quotient.\newline9m2÷m=9m9m^2 \div m = 9m
  4. Subtract and Multiply: We multiply the entire divisor (m9)(m - 9) by the new term of the quotient (9m)(9m) and subtract the result from the new dividend.\newline(9m)×(m9)=9m281m(9m) \times (m - 9) = 9m^2 - 81m\newlineSubtract this from the new dividend:\newline(9m281m)(9m281m)=0(9m^2 - 81m) - (9m^2 - 81m) = 0
  5. Final Quotient: Since we have no remainder, the division process is complete. The quotient is the sum of the terms we found: 5m2+9m5m^2 + 9m

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