SOLUTION: Are there two integers with a product of negative 16 and a sum of negative 4?

Algebra.Com
Question 896901: Are there two integers with a product of negative 16 and a sum of negative 4?
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
x*y=-16,
x+y=-4
y=-x-4
x*(-x-4)=-16
-x^2-4x+16=0
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Start with the given expression.



Factor out the GCF .



Now let's try to factor the inner expression



---------------------------------------------------------------



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 :

1,2,4,8,16

-1,-2,-4,-8,-16



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



These factors pair up and multiply to .

1*(-16) = -16
2*(-8) = -16
4*(-4) = -16
(-1)*(16) = -16
(-2)*(8) = -16
(-4)*(4) = -16


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



First NumberSecond NumberSum
1-161+(-16)=-15
2-82+(-8)=-6
4-44+(-4)=0
-116-1+16=15
-28-2+8=6
-44-4+4=0




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



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





Answer:



So simply factors to



In other words, .
RELATED QUESTIONS

Two negative integers have a sum of -12 and a product of 11. What are the integers? (answered by ankor@dixie-net.com)
two negative integers have a sum of -13 and a product of 42. what are the... (answered by Cromlix)
Two negative integers have a sum of -12 and a product or 11. What are the integers?... (answered by ewatrrr,Alan3354)
two integers have a difference of negative 11 and a sum of negative 3. what are the... (answered by deborabr)
Could you please help me with these 2 problems. They don't seem workable to me. A.... (answered by Alan3354)
two consecutive negative integers have a product of 240. what are the integers? n=... (answered by checkley77)
are there two integers with a product of -12 and a sum of... (answered by stanbon)
Two negative consecutive integers have a sum of -45. what are the integers? (answered by Alan3354)
The sum of a negative number, 1/4 of the negative number, and 7/16 of the negative number (answered by ankor@dixie-net.com)