Please Help! I don't understand the question asking.
The greatest common factor of 12m^5n^3 + 18m^3n^3 - 24m^2n^3 is Am^bn^c, where A,B and C are whole numbers?
12 = (1*12), (2*6), (3*4).
18 = (1*18), (2*9), (3*6).
24 = (1*24), (2*12), (3*8), (4*6).
CF = 1,2,3,6.
GCF = 6.
So we factor out 6 and the variables with the lowest exponents:
6m^2n^3(2m^3 + 3m - 4)
I, normally, find the GCF by knowing that the GCF =< 12 (the smallest coefficient). If 12 is too large, try
1/2 of 12, and 1/3 of 12 and etc.
To find the greatest common factor (GCF) of the given expression, we need to find the highest power of each variable that can be divided evenly into each term.
Let's break down the expression into its terms:
12m^5n^3
18m^3n^3
-24m^2n^3
Let's analyze the powers of the variables m and n in each term:
For m:
1. The highest power of m that can be divided evenly into 12m^5n^3 is m^2 (since 2 is the largest power of m common to the coefficients).
2. The highest power of m that can be divided evenly into 18m^3n^3 is m^2 (since 2 is the largest power of m common to the coefficients).
3. The highest power of m that can be divided evenly into -24m^2n^3 is m^2 (since 2 is the largest power of m common to the coefficients).
For n:
1. The highest power of n that can be divided evenly into 12m^5n^3 is n^3 (since 3 is the largest power of n common to the coefficients).
2. The highest power of n that can be divided evenly into 18m^3n^3 is n^3 (since 3 is the largest power of n common to the coefficients).
3. The highest power of n that can be divided evenly into -24m^2n^3 is n^3 (since 3 is the largest power of n common to the coefficients).
Now, let's find the GCF by taking the smallest exponent for each variable:
For m, the smallest exponent is 2.
For n, the smallest exponent is 3.
Therefore, the GCF of the given expression is m^2n^3.
To summarize, the greatest common factor (GCF) of 12m^5n^3 + 18m^3n^3 - 24m^2n^3 is m^2n^3, where A = 1, B = 2, and C = 3 (whole numbers representing the exponents of the variables).