Final answer:
To find the greatest common factor (GCF) of 8c³ and 12c², we need to determine the highest power of the common variable, 'c', and the highest common factor of the coefficients, 8 and 12. The GCF of 8c³ and 12c² is 4c².
Step-by-step explanation:
To find the greatest common factor (GCF) of 8c³ and 12c², we need to determine the largest number or variable that divides both terms evenly. In this case, the GCF can be found by determining the highest power of the common variable, 'c', and the highest common factor of the coefficients, 8 and 12.
Step 1: Identify the powers of 'c': 8c³ = 2³c³ and 12c² = 2²·3c²
Step 2: Determine the highest power of 'c', which is c².
Step 3: Find the highest common factor of the coefficients, which is 4.
Step 4: Combine the highest power of 'c' and the highest common factor of the coefficients, resulting in the GCF of 8c³ and 12c² as 4c².