Answer :

Final answer:

The greatest common factor of 3u⁴x³-48x³ is 3x³. Removing 3x³ from each term simplifies the expression to u⁴ - 16. So, the factored form of the polynomial is 3x³(u⁴ - 16).

Explanation:

The problem 3u⁴x³-48x³ is a polynomial and can be factored by factoring out the greatest common factor from both terms. The greatest common factor for both terms is 3x³.

When you remove 3x³ from each term, you end up with 3u⁴x³/3x³ - 48x³/3x³. This simplifies to u⁴ - 16.

The final factored form of the given polynomial is therefore 3x³(u⁴ - 16).

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