Question

The product of two consecutive even integers is 8. Find the integers.

Note: each set of brackets represents one solution.

Answer 1

-4 and -2

2 and 4.

Explanation:

Let n be the first even integer.

Then the consecutive even integer will be represented by (n+2).

We know that their product is 8. So:

`n(n+2)=8`

Solve for n. Distribute:

`n^2+2n=8`

Subtract 8 from both sides:

`n^2+2n-8=0`

Factor:

`(n+4)(n-2)=0`

Zero Product Property

`n+4=0\text{ or } n-2=0`

Solve for n for each case:

`n=-4\text{ or } n=2`

Hence, we will have two correct solutions.

Case 1: -4 and -2. -4(-2) is indeed 8.

Case 2: 2 and 4. 2(4) is also 8.

Hence, our solutions are:

-4 and -2

2 and 4.