Question

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

Answer 1

`(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.