hello51147 hello51147
  • 04-02-2024
  • Mathematics
contestada

prove that the polynomial x^3 - x is divisible by 6 for whole number values of x

Respuesta :

naetonwoyev2 naetonwoyev2
  • 04-02-2024

Answer:

x^3 - x = x*(x-1)*(x+1),

so the left side is the product of three consecutive integer numbers.

Of them, at least one is a multiple of 2 and exactly one is a multiple of 3.

Hence, the product, which is x^3 - x, is divisible by 2*3 = 6.

Step-by-step explanation:

Answer Link

Otras preguntas

The graph of y = 4x - 11 is translated up 8 units. Which equation represents the translated graph? f y = 4x - 19 g y = 4x - 3 h y = 12x - 11 j y = 12x - 3
if you live 35 miles from work & drive 35 mph how long would it take to get there
The dimensions of a brick that weighs 25 N are 0.19 m × 0.07 m × 0.095 m. What pressure does the brick exert on the ground if it is resting on its largest face?
conversation between Hitler and gandhi
The Indus, Ganges, and Brahmaputra were important to ancient India because they were
Please tell me five slogans on conservation of natural vegetation.
The entire region of Northern Africa and southwest Asia has a climate generally described as?
How do u write 6 more the 7 times a number is 41 in algebraic equation??
Horace read 160 pages in 4 hours. How many pages can he read in 6 hours??
The diameter of your bicycle wheel is 25 inches. How far will you move in one turn of your wheel?