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Question 552204: How to factor: x^2 +6x+40?
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=41 | | 2 | 20 | 2+20=22 | | 4 | 10 | 4+10=14 | | 5 | 8 | 5+8=13 | | -1 | -40 | -1+(-40)=-41 | | -2 | -20 | -2+(-20)=-22 | | -4 | -10 | -4+(-10)=-14 | | -5 | -8 | -5+(-8)=-13 |
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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