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Let us first divide 7 by 3,

7/3

Here

7 = 3 × 2 + 1

i.e. Dividend = Divisor × Quotient + Remainder

We can do the same when dividing two polynomials

In Example 6 ,

We divided 3x
^{
2
}
+ x − 1 by 1 + x

Our division was

Here

Dividend = 3x
^{
2
}
+ x – 1

Divisor = x + 1

Quotient = 3x – 2

And Remainder = 1

Dividend = Divisor × Quotient + Remainder

3x
^{
2
}
+ x – 1 = (x + 1) (3x – 2) + 1

3x
^{
2
}
+ x – 1 = x (3x – 2) + 1 (3x – 2) + 1

3x
^{
2
}
+ x – 1 = 3x
^{
2
}
– 2x + 3x – 2 + 1

3x
^{
2
}
+ x – 1 = 3x
^{
2
}
+ x – 1