How to factor this
x^(3) - 8 = 0
Sorry this was posted three times because something happened with my computer
this is a difference of cubes pattern
in general
A^3 - B^2 = (A-B)(A^2 + AB + B^2)
let me know what you get.
( did you notice that 8 = 2^3 ? )
To factor the expression x^(3) - 8 = 0, you can use the difference of cubes formula. The difference of cubes formula states that for any two numbers a and b, (a^(3) - b^(3)) can be factored as (a - b)(a^(2) + ab + b^(2)).
In this case, x^(3) - 8 can be rewritten as (x)^(3) - 2^(3). Now we can see that a is x and b is 2.
Applying the difference of cubes formula, we have:
(x)^(3) - 2^(3) = (x - 2)(x^(2) + 2x + 4).
Therefore, the factored form of x^(3) - 8 = 0 is (x - 2)(x^(2) + 2x + 4) = 0.