How do you factor y^3-y^2+y-1 by grouping?

1 Answer
A08
Jun 9, 2016

(y-1)(y^2+1)

Explanation:

Given expression is
y^3-y^2+y-1

  1. On inspection we notice that first two terms have a common factor y^2.
  2. if we take out y^2 common out of these two what remains is equal to the last two terms.
  3. The last two do not have any common factor except 1.

Let us therefore group first two and last two terms. We rewrite the expression as
(y^3-y^2)+(y-1)
Taking out common factor
=> y^2(y-1)+(y-1)
Taking out the common factor (y-1) out of the two terms we obtain
=> (y-1)(y^2+1)
We have our required factors.

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