This document demonstrates how to divide two polynomials. It shows the step-by-step process of dividing the polynomial x3 + 2x2 - 4x + 3 by the polynomial x2 - 1. The quotient is x + 2 and the remainder is -3x + 5.

1. POLINOMIALS DIVISION
Let's study an example to learn
how to divide two polinomials

2. x3 + 2x2 - 4x + 3 xx33 22xx22 44xx 33 x2 -1

3. xº 3 + 2x2 - 4x + 3 xº 2 -1
x

4. x3 + 2x2 - 4x + 3 xx33 22xx22 44xx 33 x2 -1
+x x

5. x3 + 2x2 - 4x + 3 xx33 22xx22 44xx 33 x2 -1
-x3 +x x

6. x3 + 2x2 - 4x + 3 x2 -1
-x3 +x
x
2x2 - 3x + 3

7. x3 + 2x2 - 4x + 3 xx33 22xx22 44xx 33 x2 -1
-x3 x
xx + 22
2x2 - 3x + 3

8. x3 + 2x2 - 4x + 3 xx33 22xx22 44xx 33 x2 -1
-x3 x
xx + 22
2x2 - 3x + 3
+2

9. x3 + 2x2 - 4x + 3 xx33 22xx22 44xx 33 x2 -1
-x3 x
xx + 22
2x2 - 3x + 3
-2x2
+2

10. x3 + 2x2 - 4x + 3 xx33 22xx22 44xx 33 x2 -1
-x3 x
xx + 22
2x2 - 3x + 3
-2x2
+2

11. x3 + 2x2 - 4x + 3 xx33 22xx22 44xx 33 x2 -1
-x3 x
xx + 22
2x2 - 3x + 3
-2x2
+2
-3x + 5

12. x3 + 2x2 - 4x + 3 xx33 ++ 22xx22 -- 44xx ++33 x2 -1
-x3 x
Q(x) = x + 2
2x2 - 3x + 3
-2x2
+2
R(x) = -3x + 5
D x d x q x r
x x x x x x
= +
+ - + = - + + - +
( ) ( )· ( )
2 4 3 1 · 2 3 5
3 2 ( 2 ) ( ) ( )