Chapter 11.3, Problem 13P

Divide.

$\left(p^2+3p+2\right)÷\left(p+1\right)$

To determine

To divide the polynomial

Answer to Problem 13P

The solution of the polynomial are $p+2$

Explanation of Solution

Given information:

The polynomial is $\left(p^2+3p+2\right)÷\left(p+1\right)$

Calculation:

The polynomial can be obtained as

  $\begin{array}{l}\left(p^2+3p+2\right)÷\left(p+1\right)\\ =\frac{p^2+3p+2}{\left(p+1\right)}\left[\text{dividing each term by }\left(p+1\right)\right]\\ =\frac{p^2+\left(2p+p\right)+2}{\left(p+1\right)}\left[\text{write 3}p=\left(2p+p\right)\right]\\ =\frac{p^2+2p+p+2}{\left(p+1\right)}\\ =\frac{p\left(p+2\right)+1\left(p+2\right)}{\left(p+1\right)}\left[\begin{array}{l}\text{the first and second term has a common factor,}p\text{ and}\\ \text{the third and fourth term has a common factor,1 on the numerator}\end{array}\right]\\ =\frac{\left(p+2\right)\left(p+1\right)}{\left(p+1\right)}\\ =p+2\left[\text{divide numerator and denominator by }\left(p+1\right)\right]\end{array}$

Hence,

The solution of the polynomial are $p+2$