Question

Which of the following lists all of the roots of
X^5 - 3x^4 + 3x^3 - x^2 =0

Why is the answer ( 0, 1)

your answer was this:
x^5 - 3x^4 + 3x^3 - x^2
= x^2(x^3-3x^2+3x-1)
= x^2(x-1)^3

but i dont get the last part..(= x^2(x-1)^3)

Answer 1

Recall Pascal's Triangle
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
...
The nth row is the coefficients of (a+b)^n
As soon as I saw 1 -3 3 -1 I knew.
Failing that, you could try plugging some values, knowing that all the roots would be +1 or -1 (See Rational Roots Theorem)