SOLUTION: How would I factor completely 9y^2-6y+6?

Algebra ->  Equations -> SOLUTION: How would I factor completely 9y^2-6y+6?      Log On


   

Question 943336: How would I factor completely 9y^2-6y+6?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
3%2A3y%5E2-2%2A3y%2B2%2A3
3%283y%5E2-2y%2B2%29

Find sensible integer combinations to try.
(3y____1)(y_____2)
Gives a 1y and a 6y. This will not give -2y.

(3y_____2)(y______1)
Gives 2y and 3y. This will not give -2y.

Next thing to try is roots for factoring the quadratic factor.
y=%286%2B-+sqrt%2836-4%2A3%2A2%29%29%2F%282%2A3%29
y=%286%2B-+sqrt%2836-24%29%29%2F6
the discriminant is 36-24=12, which will still give an irrational discriminant.

The original expression is not factorable the way you want it, but can only go as far as highlight%283%283y%5E2-2y%2B2%29%29.

The factoring can go further, but you would need to accept irrational roots.