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Divide. If there is a remainder, include it as a simplified fraction.\newline(5y2+6y)÷y(5y^2 + 6y) \div y

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Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(5y2+6y)÷y(5y^2 + 6y) \div y
  1. Divide Polynomial by Monomial: We have the expression to divide: \newline(5y2+6y)÷y(5y^2 + 6y) \div y\newlineFirst, we will divide each term in the polynomial by the monomial yy.\newline(5y2+6y)÷y=5y2y+6yy(5y^2 + 6y) \div y = \frac{5y^2}{y} + \frac{6y}{y}
  2. Divide First Term: Now let's divide the first term:\newline(5y2)/y=5y(21)=5y(5y^2)/y = 5y^{(2-1)} = 5y\newlineWe subtract the exponents because of the division property of exponents.
  3. Divide Second Term: Next, we divide the second term:\newline(6y)/y=6y(11)=6y0=6(6y)/y = 6y^{(1-1)} = 6y^0 = 6\newlineSince any non-zero number raised to the power of 00 is 11, y0y^0 is 11.
  4. Combine Results: Combine the results of the division of each term:\newline(5y2+6y)÷y=5y2y+6yy=5y+6(5y^2 + 6y) \div y = \frac{5y^2}{y} + \frac{6y}{y} = 5y + 6

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