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)   (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:

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:

and you could again check possible combinations and test them, but maybe using Discriminant is easier.


The discriminant is negative, so NO real roots, meaning IS NOT FACTORABLE.

Finally, YOUR answer is correct.
Answer by MathTherapy(10552)   (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.



 ------ Factoring out GCF, 3

This is as far as this goes, since  is PRIME. 

If you wish though, you can obtain imaginary factors by either completing the square, or

using the quadratic equation formula. 

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