Chapter 11.3, Problem 1CB

To determine

To find the quotient for $\left(x^2+6x+8\right)÷\left(x+4\right)$ .

Answer to Problem 1CB

The quotient of $\left(x^2+6x+8\right)÷\left(x+4\right)$ is $x+4$ .

Explanation of Solution

Given:

  $\left(x^2+6x+8\right)÷\left(x+4\right)$

Concept Used:

Steps to follow before applying Long Division method:

1. Write the terms of the dividend and divisor in descending powers of the variable.
2. Insert placeholders with zero coefficients for missing powers of the variable.

Calculation:

To find the quotient for $\left(x^2+6x+8\right)÷\left(x+4\right)$ use long division method.

First notice that the terms of dividend and divisor are already in descending powers of the variable.

Thus, the division may be proceeded as:

  $\begin{array}{l}x+4)x^2+6x+8(x+2\\ \underset{\_}{x^2+4x}\\ 2x+8\\ \underset{\_}{2x+8}\\ \underset{\_}{0}\end{array}$

Thus, quotient of $\left(x^2+6x+8\right)÷\left(x+4\right)$ is $x+4$ .