Chapter 11.3, Problem 2CB

To determine

To find the quotient for $\left(x^2+5x+6\right)÷\left(x+2\right)$ .

Answer to Problem 2CB

The quotient of $\left(x^2+5x+6\right)÷\left(x+2\right)$ is $x+3$ .

Explanation of Solution

Given:

  $\left(x^2+5x+6\right)÷\left(x+2\right)$

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 $\left(x^2+5x+6\right)÷\left(x+2\right)$ 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:

  $\begin{array}{l}x+2)x^2+5x+6(x+3\\ \underset{\_}{x^2+2x}\\ 3x+6\\ \underset{\_}{3x+6}\\ \underset{\_}{0}\end{array}$

Thus, quotient of $\left(x^2+5x+6\right)÷\left(x+2\right)$ is $x+3$ .