To determine the greatest common factor (GCF) of the polynomial terms 12x4, 27x3, and 6x2, we start by breaking down each coefficient and the variables.
Step 1: Factor the coefficients
– The coefficients are 12, 27, and 6.
– The prime factorization of each coefficient is as follows:
- 12 = 22 × 3
- 27 = 33
- 6 = 2 × 3
Next, we find the GCF of the coefficients 12, 27, and 6:
- The only common prime factor among these is 3.
Step 2: Determine the variable factor
– Now, let’s examine the variable part, which is x raised to different powers:
- x4 (from 12x4)
- x3 (from 27x3)
- x2 (from 6x2)
To find the GCF for the variable part, we take the lowest power of x:
- Lowest power of x = x2
Step 3: Combine the GCF of coefficients and variables
– Now combine the GCF of the coefficients and the variables:
- GCF = 3 (from coefficients) × x2 (from variables)
Final Answer:
Thus, the greatest common factor of the terms in the polynomial 12x4, 27x3, and 6x2 is 3x2.