SOLUTION: How do you factor x^2+2x-276=0?

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Question 464645: How do you factor x^2+2x-276=0?
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


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 :

1,2,3,4,6,12,23,46,69,92,138,276

-1,-2,-3,-4,-6,-12,-23,-46,-69,-92,-138,-276



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



These factors pair up and multiply to .

1*(-276) = -276
2*(-138) = -276
3*(-92) = -276
4*(-69) = -276
6*(-46) = -276
12*(-23) = -276
(-1)*(276) = -276
(-2)*(138) = -276
(-3)*(92) = -276
(-4)*(69) = -276
(-6)*(46) = -276
(-12)*(23) = -276


Now let's add up each pair of factors to see if one pair adds to the middle coefficient :



First NumberSecond NumberSum
1-2761+(-276)=-275
2-1382+(-138)=-136
3-923+(-92)=-89
4-694+(-69)=-65
6-466+(-46)=-40
12-2312+(-23)=-11
-1276-1+276=275
-2138-2+138=136
-392-3+92=89
-469-4+69=65
-646-6+46=40
-1223-12+23=11




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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