Question

What two numbers have the product of -135 and the sum of 6?

Answer 1

Step 1: Find factors of 135 

1 and 135
3 and 45
5 and 27
9 and 15

Remember the rules for multiplication involving negatives:

Multiplying a negative with a negative will always be positive.
Multiplying a negative with a positive will always be negative. 

So in order for the product to be -135, one number of each factor pair will need to be negative. 

Step 2: Figure out which factor pair will add together to get the sum of 6
(Remember at least one from each pair will be negative)

Part A: 
1 + (-135) = -134
3 + (-45) = -42
5 + (-27) = -22
9 + (-15) = -6

Part B:
135 + (-1) = 134
45 + (-3) = 42
27 + (-5) = 22
15 + (-9) = 6

(Knowing that the sum of adding a larger negative number to a smaller positive number will be negative, will make this a bit faster because you would just skip to Part B) 

The sum of 15 and -9 is 6. So there is the answer.

You can also check it, just to make sure it's the correct answer.

15 × (-9) = -135
15 + (-9) = 6