Chapter 11.5, Problem 49HP

To determine

To calculate: To write a division problem involving polynomials that would solve using long division

Answer to Problem 49HP

The quotient is $7y^4-3y^2+16$

Explanation of Solution

Given information: Two polynomials

Formula Used:

Long division is the division of whole number in a systematic procedure to derive the answer.

Calculation:

Let the polynomials be $14y^5+21y^4-6y^3-9y^2+32y+48$ and by $2y+3$

Dividing the first polynomial with the second polynomial using long division method:

  $2y+3\begin{array}{c}\hfill 7y^4-3y^2+16\\ \hfill \overline{)\begin{array}{l}14y^5+21y^4-6y^3-9y^2+32y+48\\ 14y^5+21y^4\\ --\\ -------------------\\ 0-6y^3-9y^2\\ -6y^3-9y^2\\ \text{ + }+\\ -------------------\\ 0\text{ 32}y+48\\ 16y+48\\ --\\ -------------------\\ 0\end{array}}\end{array}$

Thus, quotient is $7y^4-3y^2+16$

Conclusion:

Hence, the quotient is $7y^4-3y^2+16$