SOLUTION: I need your help factoring this problem...PLEASE! {{{(X^2 + 3X + 1)^2 -4(X^2 + 3X + 1)-5}}}

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Question 177840: I need your help factoring this problem...PLEASE!
%28X%5E2+%2B+3X+%2B+1%29%5E2+-4%28X%5E2+%2B+3X+%2B+1%29-5
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The first thing to do is to simplify this horror by letting .

Now you can substitute giving you:



Since and , this quadratic polynomial in t factors quite tidily:



Now replace t with the original expression:



Collect terms:



Now since and the first factor factors to

And since and the second factor factors to

Putting it all together:



And, as you might suspect, the graph shows four zeros that match the factors: