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math

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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)

  • math -

    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)(x-i)

    Compare that with the actual answer given.
    Looks like you just made an arthmetic error somewhere in your division.

  • math -

    3x^2+3 = 3 x(x^2 + 1) = 3(x+i)(x-i)

    You only got an overall factor of 3 wrong.

  • math -

    where does the "3" go then?

    3x^2+3 = 3 x(x^2 + 1) =

    "3"(x+i)(x-i)

    because the answer is:

    (x-1)(3x-1)(x+i)(x-i)

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