Question

1. find the lcm of

$x^2 + 5x + 6$, $x^2 + 6x + 8$, and $x^2 + 7x + 12$
\bigcirc $(x + 2)(x + 3)(x + 4)$
\bigcirc $(x + 2)(x + 3)(x + 4)^2$
\bigcirc $(x + 2)^2(x + 3)(x + 4)$
\bigcirc $(x + 2)(x + 3)^2(x + 4)$

Explanation:

Step1: Factor each quadratic

$x^2+5x+6=(x+2)(x+3)$
$x^2+6x+8=(x+2)(x+4)$
$x^2+7x+12=(x+3)(x+4)$

Step2: Identify highest power of each factor

Highest power of $(x+2)$: $1$
Highest power of $(x+3)$: $1$
Highest power of $(x+4)$: $1$

Step3: Multiply highest power factors

$\text{LCM}=(x+2)(x+3)(x+4)$

Answer:

$(x + 2)(x + 3)(x + 4)$