Question

Find the LCM of set of polynomials $n^2-7n+12,n^2-2n-8$.

Short answer

The LCM of given polynomials is $\left(n-3\right)\left(n-4\right)\left(n+2\right)$.

Step-by-step solution

Step 1. Write down the given polynomials.

The given polynomials are $n^2-7n+12,n^2-2n-8$.

Step 2. Factorize the polynomials and take common factors of each higher power.

The polynomial $n^2-7n+12$is factorized as: $\left(n-3\right)\left(n-4\right)$

The polynomial $n^2-2n-8$is factorized as: $\left(n+2\right)\left(n-4\right)$

Taking common factors of each higher power, the LCM of given polynomials is written as:

$LCM=\left(n-3\right)\left(n-4\right)\left(n+2\right)$

Step 3. Conclusion.

The LCM of given polynomials is $\left(n-3\right)\left(n-4\right)\left(n+2\right)$.