x.(x+1).(x+2).(x+3).(x+4).(x+5).(x+6).(x+7).(x+8).(x+9).(x+10).(x+11).(x+12).(x+13).(x+14).(x+15)

The given expression is:

\[
x(x+1)(x+2)(x+3)(x+4)(x+5)(x+6)(x+7)(x+8)(x+9)(x+10)(x+11)(x+12)(x+13)(x+14)(x+15)
\]

This is a product of 16 consecutive factors starting from \(x\). To simplify it, we can factor out \(x\), but the remaining expression is quite large and expanding it manually would result in a high-degree polynomial (degree 16 in \(x\)).

If you need specific analysis or a more detailed solution (like expansion or root analysis), let me know! Would you like to approach this through numerical evaluation for particular \(x\) values, or expand it step by step?

### Follow-up questions:
1. Would you like to find the roots of this polynomial?
2. Should I calculate the expansion of the entire expression?
3. Do you need any specific evaluation for particular values of \(x\)?
4. Would factoring some terms make this more manageable for you?
5. Do you need to analyze the behavior of this function at particular ranges of \(x\)?

### Tip:
Factoring or breaking the polynomial into smaller segments can simplify manual or computational handling of large products like this.

x(x+1)(x+2)(x+3)(x+4)(x+5)(x+6)(x+7)(x+8)(x+9)(x+10)(x+11)(x+12)(x+13)(x+14)(x+15)

Explore the expansion of the large polynomial x(x+1)(x+2)...(x+15), which involves 16 consecutive terms starting from x. This problem demonstrates key algebraic concepts, including polynomial factorization and product expansions, ideal for advanced high school students in Grades 11-12.

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