Question

divide. if there is a remainder, include it as a simplified fraction. (5m³ - 36m² - 81m) ÷ (m - 9)

Explanation:

Step1: Use polynomial long division

Divide the leading term of the dividend \(5m^3\) by the leading term of the divisor \(m\), we get \(5m^2\). Multiply the divisor \((m - 9)\) by \(5m^2\) to get \(5m^3-45m^2\). Subtract this from the dividend:

$$
LATEXBLOCK0
$$

Step2: Divide the new leading term

Divide the leading term of \(9m^2 - 81m\) (which is \(9m^2\)) by \(m\) to get \(9m\). Multiply the divisor \((m - 9)\) by \(9m\) to get \(9m^2-81m\). Subtract this from \(9m^2 - 81m\):

$$
LATEXBLOCK1
$$

Step3: Combine the results

The quotient from the first step is \(5m^2\) and from the second step is \(9m\), and there is no remainder. So the result of the division is \(5m^2 + 9m\).

Answer:

\(5m^2 + 9m\)