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Divide. If there is a remainder, include it as a simplified fraction. $\newline$ $(-24a^3 + 16a^2) \div 4a$

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Divide polynomials by monomials

Full solution

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

\newline

(-24a^3 + 16a^2) \div 4a

Divide $-24a^3$ by $4a$ : We have the expression $(-24a^3 + 16a^2) \div 4a$ . To divide a polynomial by a monomial, we divide each term of the polynomial by the monomial separately.
Divide $16a^2$ by $4a$ : First, divide the term $-24a^3$ by $4a$ .
$(-24a^3) \div (4a) = (-24/4) \cdot (a^3/a) = -6a^2$ .
Check that the division and simplification are correct.
Combine the results: Next, divide the term $16a^2$ by $4a$ . $\newline$ $(16a^2) \div (4a) = (\frac{16}{4}) \cdot (\frac{a^2}{a}) = 4a$ . $\newline$ Check that the division and simplification are correct.
Combine the results: Next, divide the term $16a^2$ by $4a$ .
$(16a^2) \div (4a) = (\frac{16}{4}) \cdot (\frac{a^2}{a}) = 4a$ .
Check that the division and simplification are correct.Combine the results of the two divisions to get the final answer.
$(-24a^3 + 16a^2) \div 4a = (-24a^3 \div 4a) + (16a^2 \div 4a) = -6a^2 + 4a$ .

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