Chapter 11.6, Problem 31PPS

To determine

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

Answer to Problem 31PPS

The LCM of the given pair of polynomials are $\left(x+6\right).\left(x+3\right)$

Explanation of Solution

Given:

  $\left(x^2+9x+18\right)=\left(x+6\right).\left(x+3\right)$

Calculation:

The prime factors of each expression are written below

  $\left(x^2+9x+18\right)=\left(x+6\right)\left(x+3\right)$

  $\left(x+3\right)=1.\left(x+3\right)$

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

  $LCM=\left(x+6\right).\left(x+3\right)$

Conclusion:

Therefore, the LCM of the given pair of polynomials are $\left(x+6\right).\left(x+3\right)$