Question

divide. if the polynomial does not divide evenly, include the remainder as a fraction. ((2b^{3}-26b^{2}+80b)div(b - 8))

Explanation:

Step1: Use polynomial long division

Divide the leading term of the dividend \(2b^3 - 26b^2 + 80b\) by the leading term of the divisor \(b - 8\), which is \(b\). So, \(\frac{2b^3}{b}=2b^2\).
Multiply the divisor \(b - 8\) by \(2b^2\): \(2b^2(b - 8)=2b^3 - 16b^2\).
Subtract this from the dividend: \((2b^3 - 26b^2 + 80b)-(2b^3 - 16b^2)= -10b^2 + 80b\).

Step2: Divide the new leading term

Divide the leading term of \(-10b^2 + 80b\) (which is \(-10b^2\)) by \(b\), we get \(\frac{-10b^2}{b}=-10b\).
Multiply the divisor \(b - 8\) by \(-10b\): \(-10b(b - 8)=-10b^2 + 80b\).
Subtract this from \(-10b^2 + 80b\): \((-10b^2 + 80b)-(-10b^2 + 80b)=0\).

Step3: Combine the results

Since there is no remainder, the result of the division is the sum of the terms we found in each step, which is \(2b^2 - 10b\).

Answer:

\(2b^2 - 10b\)