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Chapter 9: Q21. (page 483)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Write down the given polynomials.

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

02

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

The polynomial $n^{2} - 7 n + 12$ is factorized as: $(n - 3) (n - 4)$

The polynomial $n^{2} - 2 n - 8$ is factorized as: $(n + 2) (n - 4)$

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

$L C M = (n - 3) (n - 4) (n + 2)$

03

Step 3. Conclusion.

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

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