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Question: How can you tell if you have completely factored a polynomial?

My answer: If the elements don’t share a common factor then the polynomial is completely factored.

 

Is this correct? I don't remember how to know if a polynomial has been factored completely.

 Feb 12, 2019
 #1
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You are correct....if we take out the GCF and the remaining terms share no other common factor....it is completely factored

 

 

cool cool cool

 Feb 12, 2019
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Okay. Great! Thank you so much. I wasn't sure.

Guest Feb 12, 2019
 #3
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That seems a bit simplistic Chris. How do you know you have the GCF?  

For instance      \(x^2+3x+2\)   is not fully factored.

Melody  Feb 12, 2019
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If a polynomial is of degree n then there are n factors. Some could be double or triples or whatever, they do not have to be all distinct and they do not have to be all real. 

If you do not count complex or imaginary numbers then it can be hard to know if you have fully factored your polynomial.

 

Maybe another mathematician might like to comment further.

 Feb 12, 2019

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