Wat is (6x ^ {4} - 5x ^ {3} - 18x ^ {2} - 5x + 2) - :( 3x + 22)?

Antwoord:

# 2x ^ 3- (49x ^ 2) / 3 + (1024x) / 9-22573 / 27 + 496660 / (27 (3x + 22)) #

Uitleg:

Dit is vrij lang en ik hoop dat je dit kunt volgen.

# (6x ^ 4) / (3x) = 2 x ^ 3 # (dit is onze eerste termijn)

# 2x ^ 3 (3x + 22) = 6x ^ 4 + 44x ^ 2 #

# 6x ^ 4-5x ^ 3-18x ^ 2-5x + 2- (6x ^ 4 + 44x ^ 2) = 6x ^ 4-5x ^ 3-18x ^ 2-5x + 2-6x ^ 4-44x ^ 2 = -49x ^ 3-18x ^ 2-5x + 2 #

# - (49x ^ 3) / (3x) = - (49x ^ 2) / 3 # (dit is onze tweede termijn)

# - (49x ^ 2) / 3 (3x + 22) = - (49x ^ 2) / 3- (1078x ^ 2) / 3 #

# -49x ^ 3-18x ^ 2-5x + 2 - (- (49x ^ 2) / 3- (1078x ^ 2) / 3) = - 49x ^ 3-18x ^ 2-5x + 2 + (49x ^ 2) / 3 + (1078x ^ 2) / 3 = (1024x ^ 2) / 2 + 3-5x #

# ((1024x ^ 2) / 3) / (3x) = (1024x) / 9 # (dit is onze derde termijn)

# (1024x) / 9 (3x + 22) = (1024x ^ 2) / 3 + (22528x) / 9 #

# (1024x ^ 2) / 3-5x + 2 - ((1024x ^ 2) / 3 + (22528x) / 9) = (1024x ^ 2) / 3-5x + 2- (1024x ^ 2) / 3- (22528x) / 9 = - (22573x) / 9 + 2 #

# - ((22573x) / 9) / (3x) = - 22573/27 # (dit is onze vierde termijn)

# -22573/27 (3x + 22) = - (22573x) / 27-496606 / 27 #

# - (22573x) / 9 + 2 - (- (22573x) / 27-496606 / 27) = - (22573x) / 9 + 2 + (22573x) / 27 + 496606/27 = 496660/27 #

# 496660 / (27 (3x + 22)) # (dit is onze laatste termijn)

Dit geeft ons:

# 2x ^ 3- (49x ^ 2) / 3 + (1024x) / 9-22573 / 27 + 496660 / (27 (3x + 22)) #