Okay, no problem. Let me try to simplify the explanation:

The fundamental theorem of algebra states that every polynomial equation of degree n has n complex solutions. In other words, for any polynomial equation, you can find at least one complex number that makes the equation true.

The proof shows that if a polynomial of degree n does not have any complex solutions, then it can be factored into n linear factors with real coefficients. Since we know that every real polynomial can be factored into linear factors, this means that the original polynomial must have had complex solutions.

So in short, the proof shows that if a polynomial cannot be factored into linear factors with real coefficients, then it must have complex solutions. And since every polynomial can be factored, this proves that every polynomial has at least one complex solution.

Does this help clarify the proof? Let me know if you have any other questions!
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