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:)!
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
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
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
To factor the given expression completely, let's start by grouping the terms:
x^3 - 6x^2 + 12x - 8
Now, let's factor by grouping:
(x^3 - 6x^2) + (12x - 8)
x^2(x - 6) + 4(3x - 2)
Now, we can see that both terms have a common factor:
x^2(x - 6) + 4(3x - 2)
x^2(x - 6) + 4(3)(x - 2)
Next, we can factor out the common factor (x - 2):
x^2(x - 6) + 4(3)(x - 2)
(x - 2)(x^2 - 6x + 12)
Now, we need to check if the quadratic term (x^2 - 6x + 12) can be factored further. However, it cannot be factored since it does not have real roots. Therefore, the factored form of the given expression is:
(x - 2)(x^2 - 6x + 12)
So, it seems like the answer you provided is indeed correct: (x - 2)(x^2 + 2x + 4). It is possible that there was an error when comparing your answer with the given solution.