Final answer:
The factored form of the expression 1,458x^3 - 2 is (9x - 2)(81x^2 + 18x + 4), corresponding to option c.
Step-by-step explanation:
The factored form of the expression 1,458x^3 - 2 is (9x - 2)(81x^2 + 18x + 4), which corresponds to option c. To factor the expression, we first look for any common factors, and in this case there are none. Then, we can look for a common factor in each term, which is 2 in this case.
So we can factor out 2 from each term to get 2(729x^3 - 1). Now we have a difference of cubes, which can be further factored as (9x - 1)(81x^2 + 9x + 1). Therefore, the factored form is (9x - 2)(81x^2 + 18x + 4).