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Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(-3u^2 - 8u) \div u$

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Divide polynomials by monomials

Full solution

Q. Divide. If there is a remainder, include it as a simplified fraction.

\newline

(-3u^2 - 8u) \div u

Divide by u: We have the expression $(-3u^2 - 8u) \div u$ . To divide a polynomial by a monomial, we divide each term of the polynomial by the monomial. $(-3u^2 - 8u) \div u = \left(-\frac{3u^2}{u}\right) - \left(\frac{8u}{u}\right)$
Divide $-3u^2$ by $u$ : Now let's divide the first term $-3u^2$ by $u$ . $\frac{-3u^2}{u} = -3u^{2-1} = -3u$
Divide $-8u$ by $u$ : Next, we divide the second term $-8u$ by $u$ . $\frac{-8u}{u} = \frac{-8u}{u} = -8$
Combine results: Combine the results of the division of each term to get the final answer. $(-3u^2 - 8u) \div u = (-3u^2/u) - (8u/u) = -3u - 8$

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