Question 481981: Okay so I am having a brain-freeze on how to factor more challenging polynomials, how do you factor:
40k^2-112k+24
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
 Start with the given expression.
 Factor out the GCF  .
Now let's try to factor the inner expression 
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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 :
1,3,5,15
-1,-3,-5,-15
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*15 = 15
3*5 = 15
(-1)*(-15) = 15
(-3)*(-5) = 15
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 | 15 | 1+15=16 | | 3 | 5 | 3+5=8 | | -1 | -15 | -1+(-15)=-16 | | -3 | -5 | -3+(-5)=-8 |
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 simply factors to
In other words,  .
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