SOLUTION: Factor completely a^2-2ab+5

Question 751412: Factor completely
a^2-2ab+5
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 coefficient is .

Now multiply the first coefficient by the last coefficient 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 :
1,5
-1,-5

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*5 = 5
(-1)*(-5) = 5

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	5	1+5=6
-1	-5	-1+(-5)=-6

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

===============================================================

Answer:

So doesn't factor at all (over the rational numbers).

So is prime.

Note: there may be a typo, so make sure everything is typed correctly, thanks.
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