Final answer:
Finding the LCM of polynomials is necessary to add or subtract polynomials with different denominators by providing a common denominator, much like combining numerical fractions.
Step-by-step explanation:
It is necessary to find the Least Common Multiple (LCM) of polynomials in order to add or subtract polynomials. When combining polynomials with different denominators, we need a common denominator to combine them, much like we do with fractions. The LCM of the polynomial denominators allows us to write each polynomial fraction with the same denominator, facilitating their addition or subtraction.
To find the LCM of polynomials, we factor each polynomial and take each factor the greatest number of times it occurs in any of the polynomials. This method ensures that the LCM is the smallest polynomial that is a multiple of all the polynomials in question. Once we have the LCM, we can proceed to add or subtract the polynomials, which requires combining like terms and simplifying if necessary.
LCM is not used for squaring polynomials, multiplying polynomials, or dividing polynomials directly, but it is crucial for the addition and subtraction of polynomial expressions to ensure that operations are carried out properly.