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Divide. If there is a remainder, include it as a simplified fraction.\newline(8p224p)÷4p(8p^2 - 24p) \div 4p

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Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(8p224p)÷4p(8p^2 - 24p) \div 4p
  1. Divide by 44p: We have the expression to divide: \newline(8p224p)÷4p(8p^2 - 24p) \div 4p\newlineFirst, we will divide each term in the polynomial by the monomial 4p4p.\newline(8p224p)÷4p=8p24p24p4p(8p^2 - 24p) \div 4p = \frac{8p^2}{4p} - \frac{24p}{4p}
  2. Divide first term: Now let's divide the first term:\newline(8p2)/(4p)=8/4×p2/p=2×p=2p(8p^2)/(4p) = 8/4 \times p^2/p = 2 \times p = 2p\newlineThis is because 88 divided by 44 is 22, and p2p^2 divided by pp is pp.
  3. Divide second term: Next, we divide the second term:\newline(24p)/(4p)=24/4×p/p=6×1=6(24p)/(4p) = 24/4 \times p/p = 6 \times 1 = 6\newlineThis is because 2424 divided by 44 is 66, and pp divided by pp is 11.
  4. Combine results: Now we combine the results of the division of each term:\newline(8p2)/(4p)(24p)/(4p)=2p6(8p^2)/(4p) - (24p)/(4p) = 2p - 6\newlineThis is the simplified form of the original expression after division.

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