SOLUTION: If the product of a positive even integers equal 120 what are the two intergers?

Question 344690: If the product of a positive even integers equal 120 what are the two intergers?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Let x = the first even integer. Since even integers are 2 apart from each other, then the next even integer after x will be: x+2.
The product of these two integers would be: x * (x+2)
And we want this product to be 120. So the equation we'll use is:
x * (x+2) = 120

To solve this we'll start by simplifying the left side:

This is a quadratic equation, because of the , so we want one side of the equation to be zero. Subtract 120 from each side:

Then we'll factor (or use the Quadratic Formula):

From the Zero Product property we know that this (or any) product can be zero only if one (or more) of the factors is zero. So
x + 12 = 0 or x - 10 = 0
Solving these we get:
x = -12 or x = 10
Remembering that x is the first integer and that x+2 is the second integer we get the following pairs of even integers:
-12 and -10
10 and 12

Since we are asked to find only positive even integers, we will discard the pair of negative even integers. The positive even integers whose product is 120 are 10 and 12.
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