Chapter SH, Problem 11.5.14EP

To determine

The solution of the given expression.

Answer to Problem 11.5.14EP

  $4b^2-b+2$

Explanation of Solution

Given:

The given expression is:

  $\left(4b^3+7b^2-2b+4\right)÷\left(b+2\right)$

Calculation:

The expression cannot be factored, therefore using long division; the expression can be simplified as:

  $\begin{array}{l}b+2\begin{array}{c}\hfill 4b^2-b+2\\ \hfill \overline{)4b^3+7b^2-2b+4}\end{array}\\ \underset{\_}{4b^3+8b^2}\\ -b^2-2b\\ \underset{\_}{-b^2-2b}\\ 4\\ \underset{\_}{2b+4}\\ -2b\end{array}$

Hence, quotient will be $4b^2-b+2$