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The theorem is :

Any polynomial can be written as the product of linear factors and irreducible quadratic factors.

I did not find an intuitive proof of this theorem.I asked a question in this link http://math.stackexchange.com/questions/1158560/need-of-an-intuitive-proof-of-an-algebraic theorem

and an answer was given there but I did not fully understand this.Can anyone prove the theorem intuitively?