How to find roots of (x-1)^3-(x-1)^2?

Question

Here's what I've done so far:
(x-1)(x-1)(x-1)-(x-1)(x-1) <-- If there's an easier way, please tell =)
(x2-2x+1)(x-1)-(x2-2x+1)
x3-x2-2x2+2x+x-1-x2+2x-1
x3-4x2+5x-2...

I can't factor anything out )=...

THANK you guys! It means a lot.

Answer 1

( x - 1 ) ² [ ( x - 1 ) - 1 ]
( x - 1 ) ² ( x - 2 )

Answer 2

The trick to this problem is to not solve it in the straightforward way, but rather notice that each term is (x-1) to a power. If we declared another variable, say t, and declare that t=x-1, we could rewrite this problem as t^3-t^2. Then we could factor t^2 out of each term, giving us t^2(t-1) =0 (I'm assuming it's equal to 0 as we're finding the roots). So, the roots of t^3-t^2 are t=0, 0, or 1. If we substitute back, we get x-1=0, x-1=0, and x-1=1, thus x=1, 1, and 2.

Answer 3

Here's what you have done so far:
(x-1)(x-1)(x-1)-(x-1)(x-1) =0
Take (x-1)(x-1) common, we get
[(x-1)(x-1)] * [(x-1)-1] = 0
or (x-1)^2 * (x-2) =0

So either (x-1)^2 = 0 or x= 1 or x-2=0 or x=2.
So the roots are x= 1, 1 ,2.

Note that x has a double root at 1.

Answer 4

Do you mean (x-1)^3 - (x-1)^2 = 0 ?

then (x-1)^2(x-1-1) =0 [taking (x-1)^2 as common]

therefore (x-1)^2 = 0 or (x -2) =0 which gives

x=1 or x =2

Answer 5

(x-1)^3-(x-1)^2
(x-1)^2 [(x-1)-1]
(x-1)^2 [x-2]

Answer 6

Oh, just square all the square roots. when you square something that is square rooted, it gets rid of the square roots. √(x+1)+ √(12-x) = √(13+x) (√(x+1))squared+ (√(12-x))squared = (√(13+x))squared it then becomes a normal equation x+1+ 12-x = 13+x

Answer 7

Set the polynomial equal to zero and solve it.

(x-1)^3 - (x-1)^2 = 0

Solve it from there.

Or if you have a graphing calculator graph the function and see where the x-intercepts are.

Answer 8

(x-1)^3-(x-1)^2
(x-1)^2[(x-1)-1]
f(x)=(x-1)^2 * (x-2)
f(x)=0, therefore x=1(double root), x=2

Answer 9

take common factor (x-1)^2, you get
(x-1)^2(x-1) - (x-1)^2=
(x-1)^2(x-1-1) =
(x-1)^2(x-2)

Answer 10

(x-1)^3-(x-1)^2
= (x-1)^2 * [ (x-1) - 1 ]
= (x-1)^2 * (x-2) = 0

ans x=1
and x=2