Proving x^4 + 6x^3 + 11x^2 + 6x + 1 isn't factorable on the integers

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Ilikebugs

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I need to prove that x^4+6x^3+11x^2+6x+1 isn't factorable on the integers but I don't know where to start. Help!
 
If you have heard of the Rational Root Theorem, you should see immediately that (x-1) and (x+1) are the ONLY candidates for Integer-based factors.

Synthetic Division can help you in your exploration.
 
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Ilikebugs said:
I need to prove that x^4+6x^3+11x^2+6x+1 isn't factorable on the integers but I don't know where to start. Help!
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To learn how to find all potential rational roots, please try here. To learn how to use synthetic division to test those possibilities, please try here. After you have studied at least two lessons from each listing, please attempt the exercise.

If you get stuck, please reply showing your steps so far, so we can see what's going on and provide useful feedback. Thank you! ;)
 
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