Final answer:
To determine which of the given polynomials is completely factored, we need to check if each polynomial can be simplified further. The polynomial that is completely factored is Option C: g³ - 3g² + 2g - 5.
Step-by-step explanation:
To determine which of the given polynomials is completely factored, we need to check if each polynomial can be simplified further. A polynomial is completely factored when it cannot be factored any further.
A) g⁵ - 4g³ + 18g² + 20g² - 6g² + 5g + 420
Combining like terms, we get: g⁵ + 12g² + 5g + 420
This polynomial is not completely factored because it can still be simplified further.
B) 2g² - 6g⁴ + 5g + 420
Combining like terms, we get: -6g⁴ + 2g² + 5g + 420
This polynomial is not completely factored because it can still be simplified further.
C) g³ - 3g² + 2g - 5
This polynomial is completely factored because it cannot be simplified any further.
D) 3g² + 4g - 6
This polynomial is completely factored because it cannot be simplified any further.
Therefore, the polynomial that is completely factored is Option C: g³ - 3g² + 2g - 5.