Question

divide. if there is a remainder, include it as a simplified fraction. (18m³ - 2m) ÷ (3m + 1)

Explanation:

Step1: Use polynomial long division

Divide the leading term of the dividend \(18m^3\) by the leading term of the divisor \(3m\): \(\frac{18m^3}{3m} = 6m^2\).
Multiply the divisor \(3m + 1\) by \(6m^2\): \(6m^2(3m + 1)=18m^3 + 6m^2\).
Subtract this from the dividend: \((18m^3 - 2m)-(18m^3 + 6m^2)= - 6m^2 - 2m\).

Step2: Divide the new leading term

Divide the leading term of \(-6m^2\) by \(3m\): \(\frac{-6m^2}{3m}=-2m\).
Multiply the divisor \(3m + 1\) by \(-2m\): \(-2m(3m + 1)=-6m^2 - 2m\).
Subtract this from \(-6m^2 - 2m\): \((-6m^2 - 2m)-(-6m^2 - 2m)=0\).

Answer:

\(6m^2 - 2m\)