Chapter 11.6, Problem 32PPS

To determine

To find: the LCM of the given pair of polynomials.

Answer to Problem 32PPS

The LCM of the given pair of polynomials are $\left(k-4\right).\left(k+2\right).\left(k+2\right)$

Explanation of Solution

Given:

  $\left(k^2-2k-8\right),{\left(k+2\right)}^2$

Calculation:

The prime factors of each expression are written below

  $\left(k^2-2k-8\right)=\left(k-4\right).\left(k+2\right)$

  ${\left(k+2\right)}^2=\left(k+2\right).\left(k+2\right)$

Now, the LCM of the given pair of polynomials is calculated below

  $LCM=\left(k-4\right).\left(k+2\right).\left(k+2\right)$

Conclusion:

Therefore, the LCM of the given pair of polynomials are $\left(k-4\right).\left(k+2\right).\left(k+2\right)$