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Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(-a^3 - 4a^2) \div a^2$

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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

(-a^3 - 4a^2) \div a^2

Divide by $a^2$ : We have the expression $(-a^3 - 4a^2) \div a^2$ . To divide a polynomial by a monomial, we divide each term of the polynomial by the monomial separately. $(-a^3 - 4a^2) \div a^2 = \frac{-a^3}{a^2} + \frac{-4a^2}{a^2}$
Divide $-a^3$ : Now let's divide the first term $(-a^3)$ by $a^2$ . $\newline$ $(-a^3)/a^2 = -a^{(3-2)} = -a^1 = -a$
Divide $-4a^2$ : Next, we divide the second term $(-4a^2)$ by $a^2$ . $\frac{-4a^2}{a^2} = -4 \times \left(\frac{a^2}{a^2}\right) = -4 \times 1 = -4$
Combine Results: Combine the results of the division of each term to get the final answer. $\newline$ $(-a^3 - 4a^2) \div a^2 = \frac{-a^3}{a^2} + \frac{-4a^2}{a^2} = -a - 4$

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