Respuesta :
Answer:
(x - 9)(x² + 9x + 81)
Step-by-step explanation:
x³ - 729 ← is a difference of cubes and factors in general as
a³ - b³ = (a - b)(a² + ab + b²)
note 729 = 9³ ⇒ a = x and b = 9
x³ - 729 = (x - 9)(x² + 9x + 81) ← in factored form
Out of the given options, only x-9 is a factor of x³-729
For the expression x - a to be a factor of the function f(x), f(a) must be equal to zero
let
[tex]f(x) = x^{3} - 729[/tex]
To confirm if x - 9 is a factor, substitute x = 9 into the function.
That is find the value of f(9)
[tex]f(9) = {9}^{3} - 729[/tex]
[tex]f(9) = 729 - 729[/tex]
[tex]f(9) = 0[/tex]
Since f(9) = 0, then x - 9 is a factor of the function
[tex] {x}^{3} - 729[/tex]
Other options are not factors of x³-729 because they do not give a reminder of 0
Learn more here: https://brainly.com/question/23007119
The given options are:
x+3
x+9
x-9
x-3
