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Divide. If there is a remainder, include it as a simplified fraction.\newline(18g34g2+18g)÷2g(-18g^3 - 4g^2 + 18g) \div 2g

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Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(18g34g2+18g)÷2g(-18g^3 - 4g^2 + 18g) \div 2g
  1. Divide by 22g: We have the expression (18g34g2+18g)÷2g(-18g^3 - 4g^2 + 18g) \div 2g. To divide a polynomial by a monomial, we divide each term of the polynomial by the monomial separately.\newline(\(-18g^33 - 44g^22 + 1818g) \div 22g = (18-18g^33/22g) - (44g^22/22g) + (1818g/22g)
  2. Divide 18g3-18g^3 by 2g2g: Now let's divide the first term: 18g3-18g^3 divided by 2g2g.\newline18g3/2g=18/2×g3/g=9g2-18g^3/2g = -18/2 \times g^3/g = -9g^2
  3. Divide 4g2-4g^2 by 2g2g: Next, we divide the second term: 4g2-4g^2 divided by 2g2g.\newline4g2/2g=4/2×g2/g=2g-4g^2/2g = -4/2 \times g^2/g = -2g
  4. Divide 1818g by 22g: Finally, we divide the third term: 18g18g divided by 2g2g. \newline18g2g=182×gg=9\frac{18g}{2g} = \frac{18}{2} \times \frac{g}{g} = 9
  5. Combine results: Combining all the results, we get the final answer: (18g34g2+18g)÷2g=9g22g+9(-18g^3 - 4g^2 + 18g) \div 2g = -9g^2 - 2g + 9

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