Dividing+Polynomials

Diving Polynomials

Method 1: Long Divison

Ex1. (5x3-7x2+2x+1)/(x+3) = 5x2 - 22x + 68 - 203/ x+3

5x2 – 22x + 68 __________________________ x+3 |5x3 – 7x2 + 22x +1 -(5x3 + 15x2) ß solve for x3 ________________________ -22x2 + 2x -(-22x2 -66x) ß Solve for x2 ___________________________ 68x +1 -(68x +204) ß solve for x= ____________________ -203 ß remainder

Ex2.

3x3 – x +1 ____________ 2x+1

3/2x2 - 3/4x +1 _____________________ 2x +1 | 3x3 + 0x2 – x +1 -(3x3 + 3/2x2) ______________________ -3/2x2 –x -(-3/2x2 -3/4x) ___________________________________ -1/4x +1 -(-1/4x -1/8 ______________________ 9/8

Method 2 : Synthetic Division

Ex1 (6x4 – 7x2 +1 ) / (x-1) k=1 1 |6 0 -7 0 1 6 6 -1 -1 0 answer à 6x3 + 6x2 –x -1 remainder à 0
 * k is the value to make (x-1) = 0
 * 6 6 -1 -1
 * ____________________________

Ex 2. (4x3 -2x2 +5x-1) / (x+2) k= -2

-2| 4 -2 5 -1 4 -10 25 -51 Answer à 4x2 -10x +25 Remainder à -51
 * -8 20 -50
 * __________________

Ex3. (2x2 – 5x +1) / (2x+1) k= -1/2

-1/2 | 2 -5 1 2 -6 4 Answer à 2x -6 Remainder à 4
 * -1 3
 * ___________