Chapter 11.5, Problem 3ACYP

To determine

To calculate: To find the quotient $\left(3x^2+9x-15\right)÷\left(x+5\right)$

Answer to Problem 3ACYP

The quotient is $3x-6+\frac{15}{x+5}$

Explanation of Solution

Given information: Expression $\left(3x^2+9x-15\right)÷\left(x+5\right)$

Formula Used:

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

Calculation:

Expression is given as

  $\left(3x^2+9x-15\right)÷\left(x+5\right)$

Dividing the polynomial with the divisor to derive the quotient and remainder

  $x+5\begin{array}{c}\hfill 3x-6\\ \hfill \overline{)\begin{array}{l}3x^2+9x-15\\ 3x^2+15x\\ --\\ -------\\ 0-6x-15\\ -6b-30\\ \text{ + +}\\ -------\\ \text{ 15}\end{array}}\end{array}$

Thus, quotient is

  $3x-6+\frac{15}{x+5}$

Conclusion:

Hence, the quotient is $3x-6+\frac{15}{x+5}$