What non-polynomial functions can be "factored"?

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In summary, The conversation discusses the proof of Euler to the Basel problem, where he uses the property of polynomial functions to factor them into smaller parts. The speaker also inquires about the possibility of other non-polynomial functions having this property and whether all periodic functions possess this property. The last part of the conversation mentions the Weierstrass factorization theorem, which explains the factorization of entire functions. The speaker expresses their need to understand this theorem better and thanks the other person for their answer.
  • #1
MAGNIBORO
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hi, and thanks for come in, sorry for bad english :frown:

I was watching a proof of euler to the basilean problem, and a part of the proof he did this

sin(x) = x ( x + π ) ( x - π ) ( x + 2π ) ( x - 2π ) ( x + 3π ) ( x - 3π) ...

i understand why, but i wanted to know what not polynomial functions they have this property and how
"factored" this functions.

also wanted to know if all periodic functions have this property.

by last
this is true?

cos(x) = ( x + π/2 ) ( x - π/2 ) ( x + π3/2 ) ( x - π3/2 ) ( x + π5/2) ( x - π5/2 ) ...

thanks.
 
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1. What is a non-polynomial function?

A non-polynomial function is a mathematical function that cannot be expressed as a polynomial, meaning it cannot be written as a finite sum of terms, each consisting of a constant multiplied by one or more variables raised to a non-negative integer power.

2. Can all non-polynomial functions be factored?

No, not all non-polynomial functions can be factored. Some non-polynomial functions, such as exponential and trigonometric functions, cannot be factored using traditional methods.

3. What is factoring a non-polynomial function?

Factoring a non-polynomial function involves finding its equivalent expression in a simpler or more convenient form. This is usually done by breaking down the function into smaller parts that can be easily manipulated or solved.

4. What are some common techniques for factoring non-polynomial functions?

Some common techniques for factoring non-polynomial functions include grouping, factoring by grouping, completing the square, and using the quadratic formula. These techniques involve manipulating the function in different ways to simplify it or make it easier to solve.

5. Why is factoring non-polynomial functions important?

Factoring non-polynomial functions is important because it allows us to solve complex equations and understand the behavior of these functions. It also helps in graphing and analyzing these functions, which is crucial in many fields of science and engineering.

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