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Divide. If there is a remainder, include it as a simplified fraction.\newline(3a2−27a)÷3a(3a^2 - 27a) \div 3a

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Full solution

Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(3a2−27a)÷3a(3a^2 - 27a) \div 3a
  1. Divide by 3a3a: We have the expression to divide: \newline(3a2−27a)÷3a(3a^2 - 27a) \div 3a \newlineFirst, we will divide each term in the polynomial by the monomial 3a3a.\newline(3a2−27a)÷3a(3a^2 - 27a) \div 3a \newline= 3a23a\frac{3a^2}{3a} - 27a3a\frac{27a}{3a}
  2. Divide 3a23a^2: Now let's divide 3a23a^2 by 3a3a:
    (3a2)/(3a)(3a^2)/(3a)
    = 3/3×a2/a3/3 \times a^2/a
    = 1×a1 \times a
    = aa
  3. Divide 27a27a: Next, we divide 27a27a by 3a3a:
    27a3a\frac{27a}{3a}
    = 273×aa\frac{27}{3} \times \frac{a}{a}
    = 9×19 \times 1
    = 99
  4. Combine Results: Combine the results of the division of each term:\newline(3a^2)/(3a) - (27a)/(3a) \(\newline= a - 9\)\newlineThis is the simplified result of the division.

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