Question

How can I solve x^3 - 5x^2 + 5x -1 = 0 ?

Answer 1

try factor by grouping

Answer 2

Try to find 1 of the zeroes

Answer 3

start with x = 1 and see what happens.

Answer 4

I know that one of the zeros is 1, but I can't factor it by grouping, I think I'm doing something wrong.

Answer 5

I'm sorry. Factoring by grouping won't work for this one. When I first looked at it, I thought it would. You are on the right track with a zero being one.

Answer 6

Now that you know x = 1 is one of the zeroes: do this:

x = 1

subtract 1 from both sides
x - 1 = 0

Now you know x - 1 is a polynomial factor. Now use polynomial division to find the quadratic.

Answer 7

Divide:

\[\frac{x^3 - 5x^2 + 5x -1}{x -1}\]