Problem of the Day
Which of the following expressions yields an even integer for any integer ?
D. $n^2+11n+18$See the Solution
First, factor all of the expressions into a product of binomials:
In choice D, we have $n$ plus an odd number times $n$ plus an even number. Thus, if $n$ is even, $n+2$ will be even, and if $n$ is odd, $n+9$ will be odd, thus guaranteeing that the product will be even whether $n$ is odd or even. The other expressions have either both odd numbers or both even numbers and thus would not necessarily produce an even product.
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