Antwoord:
# x ^ 4 + 10x ^ 3 + 35x ^ 2 + 50x + 20 #
Uitleg:
Gebruik de distributieve eigenschap:
# (X + 1) (x + 2) (x + 3) (x + 4) -4 #
# x ^ 4 + 6x ^ 3 + 11x ^ 2 + 6x + 4x ^ 3 + 24x ^ 2 + 44x +24 - 4 #
Combineer zoals voorwaarden:
# x ^ 4 + 6x ^ 3 + 11x ^ 2 + 6x + 4x ^ 3 + 24x ^ 2 + 44x +24 - 4 #
# x ^ 4 + 10x ^ 3 + 35x ^ 2 + 50x + 20 #
Daar is je antwoord!
Antwoord:
# x ^ 4 + 10x ^ 3 + 35x ^ 2 + 50x + 20 #.
Uitleg:
Laat, #p (x) = (x + 1) (x + 2) (x + 3) (x + 4) -4 #, # = {(X + 1) (x + 4)} {(x + 2) (x + 3)} - 4 #, # = {X ^ 2 + 4x + x + 4} {x ^ 2 + 3x + 2x + 6} -4 #, # = (X ^ 2 + 5x + 4) (x ^ 2 + 5x + 6) -4 #, # = (Y + 4) (y + 6) -4 ……….. y = x ^ 2 + 5x #, # = (Y ^ 2 + 6y + 4y + 24) 4 #, # = Y ^ 2 + 10j + 20 #
# = (x ^ 2 + 5x) ^ 2 + 10 (x ^ 2 + 5x) +20 … omdat, y = x ^ 2 + 5x #
# = (X ^ + 10 x 4 ^ 3 + 25x ^ 2) + (10 x ^ 2 + 50x) + 20 #, # rArr p (x) = x ^ 4 + 10x ^ 3 + 35x ^ 2 + 50x + 20 #.
