Question

The product of two consecutive even integers is 168. Find the integers.

Short answer

Two consecutive even integers whose product is 168 are 12, 14 and $-12,-14$.

Step-by-step solution

Step 1. Form a quadratic equation.

It is given that the product of two consecutive even integers is 168.

Let $n$be the first even integer and $n+2$is the second even integer. Then,

$\begin{array}{rcl}n(n+2)& =& 168\\ n^2+2n-168& =& 0\end{array}$

Step 2. Solve the equation.

Split the middle term.

$\begin{array}{rcl}{n}^2+14n-12n-168& =& 0\\ n(n+14)-12(n+14)& =& 0\\ (n-12)(n+14)& =& 0\\ n& =& 12\text{and}n=-14\end{array}$

Step 3. Determine the second even integer.

For $n=12$,

$\begin{array}{rcl}n+2& =& 12+2\\ & =& 14\end{array}$

For $n=-14$,

$\begin{array}{rcl}n+2& =& -14+2\\ & =& -12\end{array}$

Step 4. Conclusion.

Two consecutive even integers whose product is 168 are 12, 14 and $-12,-14$.