Chapter 11.3, Problem 17PPE

To determine

To divide $\left(y^2-y+2\right)÷\left(y+2\right)$ .

Answer to Problem 17PPE

The quotient for $\left(y^2-y+2\right)÷\left(y+2\right)$ is $y-3$ and remainder is 18

Explanation of Solution

Given:

  $\left(y^2-y+2\right)÷\left(y+2\right)$

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 divide $\left(y^2-y+2\right)÷\left(y+2\right)$ use long division method.

The division may be proceeded as:

  $\begin{array}{l}y+2)y^2-y+2(y-3\\ \underset{\_}{y^2+2y}\\ -3y+2\\ \underset{\_}{-3y-6}\\ \underset{\_}{18}\end{array}$

Thus, the quotient for $\left(y^2-y+2\right)÷\left(y+2\right)$ is $y-3$ and remainder is 18.