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Divide. If the polynomial does not divide evenly, include the remainder as a fraction.\newline(d311d2+18d)÷(d9)(d^3 - 11d^2 + 18d) \div (d - 9)\newline______

Full solution

Q. Divide. If the polynomial does not divide evenly, include the remainder as a fraction.\newline(d311d2+18d)÷(d9)(d^3 - 11d^2 + 18d) \div (d - 9)\newline______
  1. Set Up Long Division: First, set up the long division by writing (d311d2+18d)(d^3 - 11d^2 + 18d) under the division bar and (d9)(d - 9) outside.
  2. Divide First Terms: Divide the first term of the dividend, d3d^3, by the first term of the divisor, dd, to get d2d^2. Write d2d^2 above the division bar.
  3. Multiply and Subtract: Multiply the divisor (d9)(d - 9) by the quotient d2d^2 and write the result under the dividend: d2×(d9)=d39d2d^2 \times (d - 9) = d^3 - 9d^2.
  4. Divide New Dividend: Subtract (d39d2)(d^3 - 9d^2) from (d311d2)(d^3 - 11d^2) to get the new dividend: 2d2+18d-2d^2 + 18d.
  5. Multiply and Subtract: Divide the first term of the new dividend, 2d2-2d^2, by the first term of the divisor, dd, to get 2d-2d. Write 2d-2d above the division bar next to d2d^2.
  6. Check for Remainder: Multiply the divisor (d9)(d - 9) by the new quotient 2d-2d and write the result under the new dividend: 2d×(d9)=2d2+18d-2d \times (d - 9) = -2d^2 + 18d.
  7. Check for Remainder: Multiply the divisor (d9)(d - 9) by the new quotient 2d-2d and write the result under the new dividend: 2d×(d9)=2d2+18d-2d \times (d - 9) = -2d^2 + 18d. Subtract (2d2+18d)(-2d^2 + 18d) from (2d2+18d)(-2d^2 + 18d) to get the new dividend, which is 00. There is no remainder.

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