Factor Completely.

Question

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:)!

Answer 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

Answer 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

Answer 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