1. In this case, the division is exact and Dividend = Divisor x Quotient
Long Division of Polynomials
Example 1:
Dividend
Divisor
Quotient
In this case, the division is exact and
Dividend = Divisor x Quotient

2. Dividend = Divisor x Quotient + Remainder
Long Division of Polynomials
Example 2:
The number 7 when divided by 2 will not give an exact answer. We say that the division is not exact.
[7 = (2 x 3) + remainder 1 ]
In this case, when the division is NOT exact,
Dividend = Divisor x Quotient + Remainder

3. Definition of degree:
For any algebraic expression, the highest power of the unknown determines the degree.
For division of polynomials, we will stop dividing until the degree of the expression left is smaller than the divisor.
Algebraic Expression
Degree
2x + 1 1
x3 - 5x 3
-3x2 + x + 4 2

4. Division by a Monomial
Divide:
Rewrite:
Divide each term separately:

5. Division by a Binomial Divide: Divide using long division
Insert a place holder for the missing term x 2

6. Division of Polynomials
Division of polynomials is similar to a division sum using numbers.
Consider the division 10 ÷ 2 = 5
Consider the division ( x2 + x ) ÷ ( x + 1 ) 5 2 10 - 10 -

7. Example 1:
Example 2: - - - - -

8. 3 2 7 6 1 When the division is not exact, there will be a remainder. -
Consider the division 7 ÷ 2
Consider (2x3 + 2x2 + x) ÷ (x + 1) 3 2 7 - - 6 1 -
remainder -1
remainder

9. Example 1: - -
Degree here is not smaller than divisor’s degree, thus continue dividing -
Degree here is less than divisor’s degree, thus this is the remainder

10. Example 2: - -
Degree here is less than divisor’s degree, thus this is the remainder

11. Example 3: - -