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Divide. If there is a remainder, include it as a simplified fraction.\newline(4z3+6z2)÷z2(4z^3 + 6z^2) \div z^2

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Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(4z3+6z2)÷z2(4z^3 + 6z^2) \div z^2
  1. Divide Terms: We have the expression to divide: \newline(4z3+6z2)÷z2(4z^3 + 6z^2) \div z^2\newlineFirst, we will divide each term in the polynomial by the monomial z2z^2.\newline(4z3+6z2)÷z2=4z3z2+6z2z2(4z^3 + 6z^2) \div z^2 = \frac{4z^3}{z^2} + \frac{6z^2}{z^2}
  2. Divide First Term: Now let's divide the first term:\newline(4z3)/(z2)=4z(32)=4z(4z^3)/(z^2) = 4z^{(3-2)} = 4z\newlineWe subtract the exponents because of the division property of exponents.
  3. Divide Second Term: Next, we divide the second term: \newline(6z2)/(z2)=6z22=6z0=6(6z^2)/(z^2) = 6z^{2-2} = 6z^0 = 6\newlineSince any non-zero number raised to the power of 00 is 11, z0z^0 is 11.
  4. Combine Results: Combine the results of the division of each term: \(4z^33 + 66z^22) \div z^22 = \frac{44z^33}{z^22} + \frac{66z^22}{z^22} = 44z + 66\

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