 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.
