Chapter SH, Problem 11.6.24EP

To determine

The least common multiple of the given polynomials.

Answer to Problem 11.6.24EP

  $\left(x+1\right)\left(x+1\right)\left(x-3\right)$

Explanation of Solution

Given:

The given polynomials are:

  $x^2+2x+1,x^2-2x-3$

Calculation:

The LCM is the smallest common multiple of all the terms given. The given terms can be factorized as:

  $\begin{array}{l}{x}^2+2x+1=\left(x+1\right)\left(x+1\right)\\ x^2-2x-3=\left(x-3\right)\left(x+1\right)\end{array}$

The LCM can be calculated as:

  $LCM=\left(x+1\right)\left(x+1\right)\left(x-3\right)$