Factor by grouping.
3n3 – 12n2 + 2n – 8
To factor by grouping, we need to group terms together in pairs and factor out the greatest common factor from each pair.
3n^3 - 12n^2 + 2n - 8
First, factor out the greatest common factor from the first two terms (3n^3 and -12n^2), which is 3n^2:
3n^2(n - 4)
Next, factor out the greatest common factor from the last two terms (2n and -8), which is 2:
+ 2(n - 4)
Now we can see that both terms have a common factor of (n - 4). Factor this out of the expression:
3n^2(n - 4) + 2(n - 4)
Now we have a common factor of (n - 4), so we can factor it out:
(n - 4)(3n^2 + 2)
Therefore, the factored form of 3n^3 - 12n^2 + 2n - 8 is (n - 4)(3n^2 + 2).