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Question 216187: Hi, I'm taking an online college algebra class but can't quite recall all the review concepts and am really stuck on this problem--
Factor the expression completely:
4x^4 + 1 + 3x²
Answer: (2x² + x + 1)(2x² - x - 1)
I can't figure out how to get the answer, it won't factor like a regular trinomial and doesn't come out right if I separate out the x², for instance.
And since I've been just trying to learn online so far (my textbook hasn't arrived yet), I really don't get how each set of terms has three factors instead of two. Hope my question makes sense, my math-speak probably isn't too great.
I would really appreciate any help you can give me. And feel free to dumb it down! Also if you know where I could find more problems similar to this for practice, that would be fantastic.
Thanks--
EL
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Factor the expression completely:
4x^4 + 1 + 3x²
Answer: (2x² + x + 1)(2x² - x - 1)
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I would work it backwards. See if the product
of those two factors gives you 4x^4 + 1 + 3x^2
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(2x^2 + (x+1))(2x^2 -(x+1))
= 4x^4 - (x+1)^2
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= 4x^4 -[x^2 + 2x + 1]
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= 4x^4 - x^2 - 2x -1
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That is not the same as 4x^4 + 1 + 3x^2
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I think your problem is asking you to do
something that cannot be done.
Cheers,
Stan H.
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