what two integers have a product of -35 and a sum -2

Answer 1

Using the information given, create 2 equations with integers x and y:

(1): x*y=-35

(2): x+y=-2

Solve equation (2) for x:

(2): x=-2-y

Since we know what x is, plug that into equation (1):

(1): (-2-y)*y=-35

Distribute:

(1): -2y-y²=-35

Rearrange so equation is equal to 0:

(1): 0=y²+2y-35

Factor:

(1): 0=(y-5)(y+7)

Which gives y=5 or y=-7. Pick y=5, then use the original equation 2 to solve for x:

(1): x+5=-2

Which gives x=-7. Similarly, if you pick y=-7, then using the same process you get x=5.

This gives that your two integers are 5 and -7

Hope this helps!

Answer 2

The answer is -7 and 5. To arrive at this, examine the first condition and determine which factors of 35 will give a sum of -2 when one is negative. 7 and 5 are the only factors that allow both statements to be true.