6a)++Finding+LCM's+of+polynomials

Finding the Least Common Multiple of polynomials is very similar to finding the LCM of integers. Looking back to searching for the LCM of integers, finding the LCM of polynomials are not at all difficult. The LCM of polynomials is a crucial tool of knowledge needed to add or subtracting rational polynomials, especially when the two denominators of the two rational polynomials are not equal. It all goes back to prime factorization. When doing prime factorization with integers, we find the prime factorization of two numbers and find what the two have in common and find what multiple they have in common. It is exactly the same with polynomials but just with variables. Don't let the variables confuse you!

To add or subtract rational expressions with different denominators. Rewrite each fraction so it has the LCM as its denominator by multiplying each fraction by the value 1 in an appropriate form. Combine numerators as indicated and keep the LCM as the denominator. Simplify the result if possible.**
 * Completely factor each denominator.**[[image:file:///Users/hongda/Desktop/danhfactor12.gif]]
 * Find the least common multiple for all the denominators by multiplying together the different prime factors with the greatest exponent for each factor.

ex 1.)  First I factor the polynomials: //x//3 + 5//x//2 + 6//x// = //x//(//x//2 + 5//x// + 6) = //x//(//x// + 2)(//x// + 3), and 2//x//3 + 4//x//2 = 2//x//2(//x// + 2) . Then I list these factors out, nice and neat: x (x+2)(x+3) =
 * **Find the LCM of **[[image:DADADADA.png width="108" height="30"]]   ** and 2//x//^3 + 4//x//^2 .  **

2x^2 (x+2)(x+3)
2x^2 (x+2) =

ex 2.) FIND LCM OF: 3x^5y^3 and 6x^10y^3

LCM IS 6x^10y^3 Because you take the greatest power of each prime factor you identify: 3^1 2^1 x^10 y^3.

More Links: http://www.purplemath.com/modules/lcm_gcf.htm (you have to scroll down a bit) http://www.atozmath.com/GcdLcmPoly.aspx This one allows you to input polynomials and it will find the LCM for you!