SOLUTION: How to factor: x^2 +6x+40?

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.

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

Answer:

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

So is prime.

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