Answer:
C. (x +1)(x +3)(x +4)
Step-by-step explanation:
The least common multiple is the product of the unique factors of each of the expressions. To find it, we need to factor each expression and identify the unique factors.
__
factorization
x² +4x +3 = (x +3)(x +1)
x² +7x +12 = (x +3)(x +4)
LCM
The unique factors are (x +1), (x +3), (x +4). The LCM is their product:
LCM = (x +1)(x +3)(x +4)
_____
Additional comment
The positive sign of the constant (+3, +12) in each case tells you that the constants in the binomial factors will have the same sign. The positive sign of the linear term (+4x, +7x) in each case tells you the binomial factors will have constants with a positive sign. So, all of the answer choices that have negative constants can be eliminated.
