SOLUTION: Solve the equation by factoring. 6x^2-11x+2

Question 151531: Solve the equation by factoring.
6x^2-11x+2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, let's factor

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*12
2*6
3*4
(-1)*(-12)
(-2)*(-6)
(-3)*(-4)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	12	1+12=13
2	6	2+6=8
3	4	3+4=7
-1	-12	-1+(-12)=-13
-2	-6	-2+(-6)=-8
-3	-4	-3+(-4)=-7

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

Are you sure that the book asked you to factor ? I would double check the problem.
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