Alg.2 Factoring

Factor Completely.

x^3-6^2+12x-8.

I keep getting (x-2)(x^2 +2x+4).

But the answer is (x-2)^3.

Can someone please help me:)!

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  1. when I divide
    x^3 - 6 x^2 + 12 x - 8
    by
    (x-2)
    I get
    x^2 -4 x +4 = (x-2)^2
    Not what you got.
    moreover when I cube (x-2), I get x^3 - 6 x^2 + 12 x - 8

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  2. yeahh i said my answer was wrong but then i gave you the right answer which is (x-2)^3. So i'm asking how do i get (x-2)^3? THanks

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  3. Long division
    You got (x-2) ok
    then divide by (x-2)

    ***********x^2 -4 x + 4 ___________________________
    (x-2)|x^3 - 6 x^2 + 12 x - 8
    **** x^3 - 2 x^2
    ******-------------
    ******* 0 - 4 x^2 + 12 x - 8
    ********** -4 x^2 + 8 x
    ***********--------------
    *************0 + 4 x - 8
    *****************4 x - 8
    ******************-----------
    Remainder = 0

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