Question

19. Find the least common multiple of x² + 4x +3 and x² + 7x + 12.

Answer 1

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.

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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)

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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.