Question

divide. if there is a remainder, include it as a simplified fraction. (9b³ + 3b² - 2b) ÷ (3b - 1)

Explanation:

Step1: Use polynomial long division

Divide the leading term of the dividend \(9b^3\) by the leading term of the divisor \(3b\): \(\frac{9b^3}{3b} = 3b^2\).
Multiply the divisor \(3b - 1\) by \(3b^2\): \(3b^2(3b - 1)=9b^3 - 3b^2\).
Subtract this from the dividend: \((9b^3 + 3b^2 - 2b)-(9b^3 - 3b^2)=6b^2 - 2b\).

Step2: Divide the new leading term

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

Answer:

\(3b^2 + 2b\)