Question

1. find the lcm of $x^2 - 81$ and $x^2 - 12x + 27$.

$\bigcirc\\ (x + 9)(x - 9)(x - 3)$
$\bigcirc\\ (x - 9)$
$\bigcirc\\ (x - 9)(x - 3)$
$\bigcirc\\ (x - 9)(x - 9)(x + 3)$

Explanation:

Step1: Factor first polynomial

$x^2 - 81 = (x+9)(x-9)$ (difference of squares)

Step2: Factor second polynomial

$x^2 -12x +27 = (x-9)(x-3)$ (factoring quadratic)

Step3: Find LCM of factors

LCM takes all unique factors: $(x+9)(x-9)(x-3)$

Answer:

A. $(x+9)(x-9)(x-3)$