 Dividend, Divisor, Quotient, and Remainder
Problems will look like 
dividend divisor 
or dividend ÷ divisor, 
where the dividend and divisor are polynomials.
Problem and answer will look like 
dividend divisor 
= quotient + 
remainder divisor 
Check that the division has been performed correctly (i.e., the correct
quotient and remainder have been found) by
 quotient · divisor + remainder = dividend
 That is, multiplying the quotient by the divisor and adding in the remainder
has to result in the dividend.
Example

Problem: 
x^{2} + 5x + 9 x + 2 
Dividend: x^{2} + 5x + 9
Divisor: x + 2 

Answer: 
x + 3 + 
3 x + 2 
Quotient: x + 3
Remainder: 3 
 Note that (x + 3)(x + 2) + 3 = x^{2} + 5x + 9,
that is, quotient · divisor + remainder = dividend.
 Dividing a Polynomial by a Monomial
 To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.
That means, apply the distibutive property and simplify.
Example

3x^{2}y + 5xy^{3} + 9 3xy 
= 
3x^{2}y 3xy 
+ 
5xy^{3} 3xy 
+ 
9 3xy 

= 
x 
+ 
5y^{2} 3 
+ 
3 xy 
Answer: 
3x 
+ 
5y^{2} 
+ 
3 xy 
Example

a^{2}b^{2}c  6abc^{2} + 5a^{3}b^{5} 2abc^{2} 
= 
a^{2}b^{2}c 2abc^{2} 
 
6abc^{2} 2abc^{2} 
+ 
5a^{3}b^{5} 2abc^{2} 

= 
ab 2c 
 
3 
+ 
5a^{2}b^{4} 2c^{2} 
Answer: 
ab 2c 
 
3 
+ 
5a^{2}b^{4} 2c^{2} 
 Long Polynomial Division
 Long polynomial division may always be used when the divisor has more than one term.
That is, the divisor is a binomial or trinomial or etc.
 Long polynomial division is a technique for finding the quotient and remainder given the dividend and divisor.
 Long polynomial division is performed much like long division of numbers.
 The following examples will demonstrate how to do long polynomial division:
 Example 1
 Example 2
 Example 3
