Question 351365: How do you factor 2y^2-15y+12?
Found 2 solutions by jim_thompson5910, checkley77:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
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 :
1,2,3,4,6,8,12,24
-1,-2,-3,-4,-6,-8,-12,-24
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*24 = 24
2*12 = 24
3*8 = 24
4*6 = 24
(-1)*(-24) = 24
(-2)*(-12) = 24
(-3)*(-8) = 24
(-4)*(-6) = 24
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 | 24 | 1+24=25 | | 2 | 12 | 2+12=14 | | 3 | 8 | 3+8=11 | | 4 | 6 | 4+6=10 | | -1 | -24 | -1+(-24)=-25 | | -2 | -12 | -2+(-12)=-14 | | -3 | -8 | -3+(-8)=-11 | | -4 | -6 | -4+(-6)=-10 |
From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.
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Answer:
So doesn't factor at all (over the rational numbers).
So is prime.
If you need more help, email me at jim_thompson5910@hotmail.com
Also, feel free to check out my tutoring website
Jim
Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website! 2y^2-15y+12
Use the formula below.
y=(15+-sqrt[-15^2-4*2*12])/2*2
y=(14+-sqrt[225-96])/4
y=(15+-sqrt129)/4
y=(15+-11.3578)/4
y=(15+11.3578)/4
y=26.3578/4
y=6.589 ans.
y=(15-11.3578)/4
y=3.64/4
y=.91 ans.
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