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Divide. If there is a remainder, include it as a simplified fraction.\newline(−18k2+18k)÷2k(-18k^2 + 18k) \div 2k

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Full solution

Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(−18k2+18k)÷2k(-18k^2 + 18k) \div 2k
  1. Divide by 22k: We have the expression (−18k2+18k)÷2k(-18k^2 + 18k) \div 2k. To solve this, we will divide each term in the polynomial by the monomial 2k2k.\newline(−18k2+18k)÷2k=−18k22k+18k2k(-18k^2 + 18k) \div 2k = \frac{-18k^2}{2k} + \frac{18k}{2k}
  2. Divide −18k2-18k^2: Now let's divide the first term: (−18k2)/(2k)(-18k^2)/(2k).\newline(−18k2)/(2k)=−18/2×k2/k=−9×k=−9k(-18k^2)/(2k) = -18/2 \times k^2/k = -9 \times k = -9k
  3. Divide 1818k: Next, we divide the second term: (18k)/(2k)(18k)/(2k).(18k)/(2k)=18/2×k/k=9×1=9(18k)/(2k) = 18/2 \times k/k = 9 \times 1 = 9
  4. Combine Results: Combine the results of the division of each term to get the final answer.(−18k2+18k)÷2k=−18k22k+18k2k=−9k+9(-18k^2 + 18k) \div 2k = \frac{-18k^2}{2k} + \frac{18k}{2k} = -9k + 9

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