Question 697929: how to factor 4x^2-2x+7
Found 2 solutions by jim_thompson5910, Alan3354:
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 :
1,2,4,7,14,28
-1,-2,-4,-7,-14,-28
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*28 = 28
2*14 = 28
4*7 = 28
(-1)*(-28) = 28
(-2)*(-14) = 28
(-4)*(-7) = 28
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 | 28 | 1+28=29 | | 2 | 14 | 2+14=16 | | 4 | 7 | 4+7=11 | | -1 | -28 | -1+(-28)=-29 | | -2 | -14 | -2+(-14)=-16 | | -4 | -7 | -4+(-7)=-11 |
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.
Answer by Alan3354(69443)  (Show Source):
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