SOLUTION: How would I complete this factor 9y^2-6y+6. This is what I have so far, (3y+2)(3y+2).

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Question 943590: How would I complete this factor 9y^2-6y+6. This is what I have so far, (3y+2)(3y+2).

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
What said here is not quite right:
You should be able to find the combination of values to pick the parts of that perfect square through simple trials of possible combinations. You see "-6y", so you expect to use two negative number constants.

My mistake: cross%28%283y-2%29%5E2%29

If you are trying to factor the original expression, try looking for combinations of binomials that will work.
(3y_______1)(3y_______6)
3y and 18y
not work

(3y______2)(3y______3)
6y and 9y
not work

(9y_______1)(y________6)
54 and 1
not work

Anything else?

(9y_______6)(y_____1)
9 and 6
not work

(9y______2)(y_______3)
27 and 2
not work

(9y________6)(y_______1)
9 and 6
not work

(9y______3)(y_______2)
18 and 3
not work

THIS should be possible, should be obvious:
highlight%283%283y%5E2-2y%2B2%29%29
and you could again check possible combinations and test them, but maybe using Discriminant is easier.
%28-2%29%5E2-4%2A3%2A2
4-24%3C0
The discriminant is negative, so NO real roots, meaning 3y%5E2-2y%2B2 IS NOT FACTORABLE.

Finally, YOUR answer is correct.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

How would I complete this factor 9y^2-6y+6. This is what I have so far, (3y+2)(3y+2).

Those can't possibly be the factors since + 2 * + 2 = + 4, and not + 6. Futhermore, + 6y + 6y doesn't result in - 6y.
9y%5E2+-+6y+%2B+6
highlight_green%283%283y%5E2+-+2y+%2B+2%29%29 ------ Factoring out GCF, 3
This is as far as this goes, since 3y%5E2+-+2y+%2B+2 is PRIME.
If you wish though, you can obtain imaginary factors by either completing the square, or
using the quadratic equation formula.