factor out the greatest common factor -36m^2n^3-60mn^4+18m^4n^2
36m^2n^3 _ 60mn^4 + 18m^4N^2.
GCF =< 18.
6mn^2(6mn-10n^2+3m^3).
To factor out the greatest common factor, we need to find the highest common factor of the given terms.
In this case, the common factors are -6, m, n^2.
Step 1: Take out the common factor -6mn^2.
-6mn^2(-6mn + 10n^2 - 3m^3n)
So, the factored form of -36m^2n^3 - 60mn^4 + 18m^4n^2 is -6mn^2(-6mn + 10n^2 - 3m^3n).
To factor out the greatest common factor (GCF) of the given expression -36m^2n^3 - 60mn^4 + 18m^4n^2, we need to identify the largest common factor of the coefficients and variables in each term.
Step 1: Identify the coefficients. The coefficients in this expression are -36, -60, and 18.
Step 2: Find the greatest common factor (GCF) of the coefficients. The GCF of -36, -60, and 18 is 6 (which is the largest number that divides evenly into all three coefficients).
Step 3: Identify the variables. The variables in this expression are m and n.
Step 4: Determine the lowest exponent for each variable. The lowest exponent for m is 2 (from m^2) and for n is 3 (from n^3) since they appear in all three terms.
Step 5: Combine the GCF of the coefficients and the variables with their respective lowest exponents.
Thus, the GCF of the given expression is 6m^2n^3.
To factor out the GCF, divide each term by the GCF:
-36m^2n^3 ÷ 6m^2n^3 = -6
-60mn^4 ÷ 6m^2n^3 = -10n
18m^4n^2 ÷ 6m^2n^3 = 3m^2n^2
Therefore, the factored form of the expression -36m^2n^3 - 60mn^4 + 18m^4n^2 is 6m^2n^3(-6 - 10n + 3m^2n^2).