Question

1. find the least common multiple of $x^2 + 4x + 3$ and $x^2 + 7x + 12$.

$\boldsymbol{(x + 1)(x + 3)(x + 4)}$
$\boldsymbol{(x + 3)(x + 4)(x - 1)}$
$\boldsymbol{(x + 1)(x - 4)(x + 3)}$
$\boldsymbol{(x - 1)(x - 3)(x - 4)}$

Explanation:

Step1: Factor first polynomial

$x^2 + 4x + 3 = (x + 1)(x + 3)$

Step2: Factor second polynomial

$x^2 + 7x + 12 = (x + 3)(x + 4)$

Step3: Find LCM of factors

LCM = $(x + 1)(x + 3)(x + 4)$

Answer:

$(x + 1)(x + 3)(x + 4)$