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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