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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 likedividend
divisor
or dividend ÷ divisor,
where the dividend and divisor are polynomials.
Problem and answer will look likedividend
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 + 9
Divisor:  x + 2
Answer:x + 3 +3
x + 2
Quotient: x + 3
Remainder: 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.
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