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Divide. If there is a remainder, include it as a simplified fraction.\newline(5j3+5j2+20j)÷5j(5j^3 + 5j^2 + 20j) \div 5j

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Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(5j3+5j2+20j)÷5j(5j^3 + 5j^2 + 20j) \div 5j
  1. Divide Expression: We have the expression to divide: \newline(5j3+5j2+20j)÷5j(5j^3 + 5j^2 + 20j) \div 5j\newlineFirst, we will divide each term in the polynomial by the monomial 5j5j.\newline(5j3+5j2+20j)÷5j=5j35j+5j25j+20j5j(5j^3 + 5j^2 + 20j) \div 5j = \frac{5j^3}{5j} + \frac{5j^2}{5j} + \frac{20j}{5j}
  2. Divide First Term: Now, let's divide the first term:\newline(5j3)/(5j)=55×j3j=1×j(31)=j2(5j^3)/(5j) = \frac{5}{5} \times \frac{j^3}{j} = 1 \times j^{(3-1)} = j^2
  3. Divide Second Term: Next, we divide the second term:\newline(5j2)/(5j)=55×j2j=1×j21=j(5j^2)/(5j) = \frac{5}{5} \times \frac{j^2}{j} = 1 \times j^{2-1} = j
  4. Divide Third Term: Finally, we divide the third term: \newlineegin{equation}\newline\frac{2020j}{55j} = \frac{2020}{55} \times \frac{j}{j} = 44 \times 11 = 44\newline\end{equation}
  5. Combine Results: Combining the results from the previous steps, we get:\newline(5j3+5j2+20j)÷5j=j2+j+4(5j^3 + 5j^2 + 20j) \div 5j = j^2 + j + 4

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