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Divide. If there is a remainder, include it as a simplified fraction.\newline(2y3−4y2)÷y(2y^3 - 4y^2) \div y

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Full solution

Q. Divide. If there is a remainder, include it as a simplified fraction.\newline(2y3−4y2)÷y(2y^3 - 4y^2) \div y
  1. Divide Polynomial by Monomial: We have the expression to divide: \newline(2y3−4y2)÷y(2y^3 - 4y^2) \div y\newlineFirst, we will divide each term in the polynomial by the monomial yy.\newline(2y3−4y2)÷y=2y3y−4y2y(2y^3 - 4y^2) \div y = \frac{2y^3}{y} - \frac{4y^2}{y}
  2. Divide First Term: Now let's divide the first term (2y3)(2y^3) by yy.\newline(2y3)/y=2y(3−1)=2y2(2y^3)/y = 2y^{(3-1)} = 2y^2\newlineWe subtract the exponents because of the division property of exponents.
  3. Divide Second Term: Next, we divide the second term (−4y2)(-4y^2) by yy.\newline(−4y2)/y=−4y(2−1)=−4y(-4y^2)/y = -4y^{(2-1)} = -4y\newlineAgain, we subtract the exponents because of the division property of exponents.
  4. Combine Results: Combine the results of the division of each term.\newline(2y3−4y2)÷y=2y3y−4y2y=2y2−4y(2y^3 - 4y^2) \div y = \frac{2y^3}{y} - \frac{4y^2}{y} = 2y^2 - 4y

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