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Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(-18k^2 + 18k) \div 2k$

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Divide polynomials by monomials

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

\newline

(-18k^2 + 18k) \div 2k

Divide by $2$ k: We have the expression $(-18k^2 + 18k) \div 2k$ . To solve this, we will divide each term in the polynomial by the monomial $2k$ . $\newline$ $(-18k^2 + 18k) \div 2k = \frac{-18k^2}{2k} + \frac{18k}{2k}$
Divide $-18k^2$ : Now let's divide the first term: $(-18k^2)/(2k)$ . $\newline$ $(-18k^2)/(2k) = -18/2 \times k^2/k = -9 \times k = -9k$
Divide $18$ k: Next, we divide the second term: $(18k)/(2k)$ . $(18k)/(2k) = 18/2 \times k/k = 9 \times 1 = 9$
Combine Results: Combine the results of the division of each term to get the final answer. $(-18k^2 + 18k) \div 2k = \frac{-18k^2}{2k} + \frac{18k}{2k} = -9k + 9$

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