math
posted by william on .
how do you factor the polynomial 3x^44x^3+4x^24x+1?
i got (x1)(3x1)(3x^2+3)
but the answer is (x1)(3x1)(x+i)(xi)

You should have realized your answer was wrong by looking at the constants of your three factors.
Multiplying them would have given you a last term of +3 instead of the needed +1.
You were close, actually you are off by only a constant factor of 3
Look at your last factor of (3x^2+3)
=3(x^2+1)
=3(x+i)(xi)
Compare that with the actual answer given.
Looks like you just made an arthmetic error somewhere in your division. 
3x^2+3 = 3 x(x^2 + 1) = 3(x+i)(xi)
You only got an overall factor of 3 wrong. 
where does the "3" go then?
3x^2+3 = 3 x(x^2 + 1) =
"3"(x+i)(xi)
because the answer is:
(x1)(3x1)(x+i)(xi)