Final answer:
The greatest common factor of the terms 25x² and 15x is 5x. This is found by looking at the common numerical coefficient, which is 5, and the variable 'x' with the lowest power, which is x to the power of 1.
Step-by-step explanation:
To find the common factor of the terms 25x² and 15x, we need to identify the greatest factor that divides both terms. Both numbers 25 and 15 are multiples of 5, and since both terms have an 'x' in common with at least 1 power of x, the greatest common factor (GCF) will include this variable as well. The GCF is the product of the smallest power of common variables and the highest common factor of the coefficients.
First, let's factor out the common numerical coefficient which is 5:
- 25 is 5× 5 and 15 is 5× 3
- Both terms have 'x' but with different powers. The lowest power is x¹ (present in both terms).
Therefore, the GCF is 5x. This can be used to simplify expressions or to factor polynomials.