what is the greatest common factor of the terms of 24m^9-27m^7-24m^5
24m^9 - 27m^7 - 24m^5
= 3m^5(8m^4 - 9m^2 - 8)
so the GCF is 3m^5
To find the greatest common factor (GCF) of the terms in the expression 24m^9 - 27m^7 - 24m^5, we need to identify the highest exponent of "m" that is common to all the terms and the largest numerical coefficient that divides all the coefficients evenly.
Step 1: Identify the numerical coefficients.
In this case, the coefficients are 24 and -27 (the coefficient in front of m^9 and m^7, respectively).
Step 2: Identify the exponents of "m".
The exponents of "m" in each term are 9, 7, and 5.
Step 3: Find the GCF of the coefficients.
The GCF of 24 and -27 can be found by listing their prime factors and selecting the highest power common to both numbers. In this case, the prime factors of 24 are 2 and 3, while the prime factors of 27 are 3 and 3 (27 = 3^3). The highest exponent common to both numbers is 3, so the GCF of the coefficients is 3.
Step 4: Find the GCF of the exponents of "m".
To find the GCF of the exponents, we select the smallest exponent among the terms. In this case, the smallest exponent is 5, so the GCF of the exponents is 5.
Step 5: Combine the GCF of the coefficients and the GCF of the exponents.
The GCF of the coefficients is 3, and the GCF of the exponents is 5. Therefore, the greatest common factor (GCF) of the terms 24m^9 - 27m^7 - 24m^5 is 3m^5.