Chapter 8.2, Problem 21PPS

To determine

To find: the LCM of polynomials.

Answer to Problem 21PPS

The LCM of the polynomials is $12\left(2x-1\right)\left(2x+3\right)\left(x+4\right)$ .

Explanation of Solution

Given information:

The polynomials are $6x^2+21x-12,4x^2+22x+24$

Calculation: to find the LCM od the polynomials, first factorise the polynomials and then multiply one of each factor and repeat factors with highest exponents,

  $\begin{array}{l}6x^2+21x-12=3\left(2x-1\right)\left(x+4\right)\text{ [factor]}\\ 4x^2+22x+24=4\left(2x+3\right)\left(x+4\right)\text{ [factor]}\\ \text{LCM}=12\left(2x-1\right)\left(2x+3\right)\left(x+4\right)\text{ [multiply the common factor and each factors]}\end{array}$

Thus, the LCM of the polynomials is $12\left(2x-1\right)\left(2x+3\right)\left(x+4\right)$ .