Question

Factor completely c⁴ - 2401 ? 1) c⁴ - 2401 = 0 2) c⁴ - 2401 is prime. 3) Cannot be factored. 4) None of the above

Answer 1

The expression c⁴ - 2401 is a difference of squares and factors completely into (c² + 49)(c + 7)(c - 7), so the correct answer is 'None of the above'.

Step-by-step explanation:

To factor the expression c⁴ - 2401, we can recognize this as a difference of squares since 2401 is a perfect square (49²). The difference of squares factoring formula is a² - b² = (a + b)(a - b), where a and b are both squares. Here, a is c² and b is 49. So, the factored form of the expression is (c² + 49)(c² - 49).

Notice that c² - 49 is also a difference of squares (7²), so it can be further factored as (c² + 49)(c + 7)(c - 7). Therefore, the correct answer is None of the above, as c⁴ - 2401 can indeed be factored completely.