posted by william .
how do you factor the polynomial 3x^4-4x^3+4x^2-4x+1?
i got (x-1)(3x-1)(3x^2+3)
but the answer is (x-1)(3x-1)(x+i)(x-i)
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)
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)(x-i)
You only got an overall factor of 3 wrong.
where does the "3" go then?
3x^2+3 = 3 x(x^2 + 1) =
because the answer is: