To find the greatest common factor (GCF) of the terms in the polynomial 12x⁴, 27x³, and 6x², we need to identify both the numerical and variable parts of each term.
First, let’s break down each coefficient:
- 12 can be factored into: 2 × 2 × 3
- 27 can be factored into: 3 × 3 × 3
- 6 can be factored into: 2 × 3
Next, we determine the GCF of the coefficients:
- The common factors are: 3.
Now, let’s look at the variable parts:
- The term 12x⁴ has x raised to the power of 4.
- The term 27x³ has x raised to the power of 3.
- The term 6x² has x raised to the power of 2.
The GCF for x is x², since it’s the smallest exponent among the terms.
Putting it all together, the GCF of the entire polynomial is:
- 3x².
Therefore, the greatest common factor of the terms in the polynomial 12x⁴, 27x³, and 6x² is 3x².