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by Matt@VeritasPrep » Sun Feb 14, 2016 9:29 pm
We could also explore this conceptually:

If a number is an odd multiple of 3, we can write it as 3*(something odd) or 3 * (some even integer + 1), or 3*(2k + 1), where k is some integer we don't care about. (It just stands for any integer.)

So our number is of the form 6k + 3.

We know that y = (6k + 3)Â² + 3(6k + 3), or y = 36kÂ² + 36k + 9 + 18k + 9, or y = 36kÂ² + 54k + 18.

We can see that 18 factors out: y = 18 * (2kÂ² + 3k + 1)

but that 4, 8, and 36 do not, so D is our pick.

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