#### Read the introductory example

#### Collapse the introductory example

Let $A=x^{3}+2x^{2}-1$ and $B=x^{2}-x+1$. Then we can write

\[A=BQ+R\]

where $Q=x+3$ and $R=2x-4$ are called the quotient and the remainder, respectively. You may verify the above equation by expanding and simplifying the right-hand side.

In general, if $A$ and $B$ are two polynomials such that $\text{degree}(B)\leq \text{degree}(A)$, then there are unique polynomials $Q$ and $R$ such that

\[A=BQ+R\]

where $\text{degree}(R)<\text{degree}(B)$.

- The process of finding $Q$ and $R$ is called the process of dividing $A$ by $B$.
- In this process, $A$ is called the
*dividend*, $B$ the*divisor*, $Q$ the*quotient*, and $R$ the*remainder*. If $R=0$, we say $A$ is**divisible**by $B$.

## Long Division of Polynomails

How the quotient and the remainder are obtained is best explained in the following example.

Now try to solve the following example.