Het quotiënt van de deling
van   x5 + 2x − x4 − 1
door   x + 1 + x3
is 		A.   x2 − x
B.   − x2 + 2
C.   x2 − x − 2
D.   x2 − x + 1
E.   x2 − 1
                 

[ 3-1583 - op net sinds 21.11.12-(E)-27.12.2023 ]

Translation in   E N G L I S H

If you divide
the polynomial
x5 + 2x − x4 − 1
by   x + 1 + x3
the quotient is 		A.  x2 − x
B.  −x2 + 2
C.  x2 − x − 2
D.  x2 − x + 1
E.  x2 − x − 1

Oplossing - Solution

Deeltal :   x5 − x4 + 2x − 1 = x5 − x4 + 0x3 + 0x2 + 2x − 1
Deler :     x3 + x + 1
x5 − x4 + 0x3 + 0x2 + 2x − 1   | x3 + x + 1
x5     + x3   +  x2      |x2 − x − 1   → quotiënt
  −x4  −x3  −x2 + 2x
  −x4      − x2 − x
      −x3     + 3x  − 1
      −x3     − x    − 1
          + 4x   → rest van de deling
GWB