Question 687132: how do u factor 2w^2+13w-20 im having trouble
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 :
1,2,4,5,8,10,20,40
-1,-2,-4,-5,-8,-10,-20,-40
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*(-40) = -40
2*(-20) = -40
4*(-10) = -40
5*(-8) = -40
(-1)*(40) = -40
(-2)*(20) = -40
(-4)*(10) = -40
(-5)*(8) = -40
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 | -40 | 1+(-40)=-39 | | 2 | -20 | 2+(-20)=-18 | | 4 | -10 | 4+(-10)=-6 | | 5 | -8 | 5+(-8)=-3 | | -1 | 40 | -1+40=39 | | -2 | 20 | -2+20=18 | | -4 | 10 | -4+10=6 | | -5 | 8 | -5+8=3 |
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.
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