Final answer:
To find two consecutive even integers whose product is 168, we set up and solved the equation n(n + 2) = 168, which yielded n = 12 and n + 2 = 14. Hence, the integers are 12 and 14.
Step-by-step explanation:
The product of two consecutive even integers being 168 requires us to set up an algebraic equation. Let's denote the first even integer as n. Since we are dealing with consecutive even integers, the next integer would be n + 2. The product of these integers is given to be 168, so our equation is n * (n + 2) = 168.
Expanding this we get n^2 + 2n - 168 = 0. Factoring the quadratic equation, we find that (n + 14)(n - 12) = 0. Therefore, the values of n that satisfy this equation are -14 and 12. We are interested in the positive solution since integer sizes are always positive, so the first integer is 12. Consequently, the second integer is 12 + 2 = 14. Therefore, the two consecutive even integers are 12 and 14.