Chapter 6.7, Problem 6OE

To determine

To calculate: the dividend.

Answer to Problem 6OE

The dividend is $2x^3+9x+5$.

Explanation of Solution

Given information:

  $\begin{array}{l}divisor=x^2+1\\ quotient=2x\\ remainder=7x+5\end{array}$

Formula used:

  $\frac{Dividend}{Divisor}=Quotient+\frac{\mathrm{Re}mainder}{Divisor}$ .

Or

  $Dividend=Quotient\times Divisor+\mathrm{Re}mainder$

Calculation:

Consider ,

  $\begin{array}{l}divisor=x^2+1\\ quotient=2x\\ remainder=7x+5\end{array}$

Now,

  $dividend=2x(x^2+1)+7x+5$

  $\begin{array}{l}=2x(x^2)+2x+7x+5\\ =2x^3+9x+5\end{array}$

Thus, the dividend is $2x^3+9x+5$.