Chapter 11.5, Problem 1CCYP

To determine

To calculate: To solve $\left(4r^6+3r^4-2r^2\right)÷2r$

Answer to Problem 1CCYP

  $\left(4r^6+3r^4-2r^2\right)÷2r=2r^5+1.5r^3-r$

Explanation of Solution

Given information: Expression $\left(4r^6+3r^4-2r^2\right)÷2r$

Formula Used:

As per the distributive property,

  $\left(a-b\right)÷c=\left(a÷c\right)-\left(b÷c\right)$

  $\left(a+b\right)÷c=\left(a÷c\right)+\left(b÷c\right)$

  $\left(a\times b\right)÷c=\left(a÷c\right)\times \left(b÷c\right)$

  $\left(a÷b\right)÷c=\left(a÷c\right)÷\left(b÷c\right)$

Calculation:

Expression is given as

  $\left(4r^6+3r^4-2r^2\right)÷2r$

On solving the above expression:

  $\begin{array}{l}\Rightarrow \left(4r^6÷2r\right)+\left(3r^4÷2r\right)-\left(2r^2÷2r\right)\\ \Rightarrow \left(\frac{4r^6}{2r}\right)+\left(\frac{3r^4}{2r}\right)-\left(\frac{2r^2}{2r}\right)\\ \Rightarrow \left(\frac{2r^5}{1}\right)+\left(\frac{3r^3}{2}\right)-\left(\frac{r}{1}\right)\\ \Rightarrow 2r^5+1.5r^3-r\end{array}$

Conclusion:

Hence, $\left(4r^6+3r^4-2r^2\right)÷2r=2r^5+1.5r^3-r$