If n is a positive even integer, then what are the GCF and LCM of the expressions n² + 5n + 6 and n² + 3n + 2?
Solution: Just as with numbers, you need to compare the factors.
n² + 5n + 6 = (n + 2)(n + 3)
n² + 3n + 2 = (n + 2)(n + 1)
(n + 2) is a common factor, while (n + 3) and (n + 1) are two consecutive odd integers. The GCF of two consecutive odd integers is 1, because if we divide (n + 3) by any factor of (n + 1), the remainder will be 2.
Therefore the GCF of n² + 5n + 6 and n² + 3n + 2 is (n + 2).
The least common multiple will be the product (n + 2)(n + 3)(n + 1). The answer choices may leave the expressions as factors, or may multiply the factors: n³ + 6n² + 11n + 6  Could you explain the solution a little better. I'm confused because I thought the GCF was n² + 2, would you mind explaining. Thanks.
