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## Sunday, 24 March 2013

### Intermediate Algebra chapter 5 part 3

Polynomial Division
Chapter 5
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: x2 + 5x + 9 x + 2 Dividend: x2 + 5x + 9Divisor:  x + 2
 Answer: x + 3 + 3 x + 2 Quotient: x + 3Remainder: 3
Note that (x + 3)(x + 2) + 3 = x2 + 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
 3x2y + 5xy3 + 9 3xy = 3x2y 3xy + 5xy3 3xy + 9 3xy = x + 5y2 3 + 3 xy
 Answer: 3x + 5y2 + 3 xy
Example
 a2b2c - 6abc2 + 5a3b5 2abc2 = a2b2c 2abc2 - 6abc2 2abc2 + 5a3b5 2abc2 = ab 2c - 3 + 5a2b4 2c2
 Answer: ab 2c - 3 + 5a2b4 2c2

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.