To determine the common factor of the terms [tex]\( 15x^2 - 12x \)[/tex], let's break down the terms carefully:
1. The first term is [tex]\( 15x^2 \)[/tex].
2. The second term is [tex]\( -12x \)[/tex].
### Step 1: Identify the Numerical Coefficients
First, let's look at the numerical coefficients of each term:
- The coefficient of the first term ([tex]\( 15x^2 \)[/tex]) is 15.
- The coefficient of the second term ([tex]\( -12x \)[/tex]) is -12.
### Step 2: Find the Greatest Common Divisor (GCD) of the Coefficients
The next step is to find the greatest common divisor (GCD) of the coefficients 15 and -12.
- The factors of 15 are 1, 3, 5, and 15.
- The factors of 12 are 1, 2, 3, 4, 6, and 12.
- The greatest common factor among these numbers is 3.
### Step 3: Identify the Variable Part
Now, let's consider the variable part of each term:
- The first term [tex]\( 15x^2 \)[/tex] has [tex]\( x^2 \)[/tex].
- The second term [tex]\( -12x \)[/tex] has [tex]\( x \)[/tex].
In both terms, the minimum power of [tex]\( x \)[/tex] present is [tex]\( x \)[/tex].
### Step 4: Combine the GCD and the Variable Part
Combining the GCD of the numerical coefficients (which is 3) and the minimum power of [tex]\( x \)[/tex] (which is [tex]\( x \)[/tex]), the common factor of both terms is [tex]\( 3x \)[/tex].
Therefore, the common factor of the polynomial [tex]\( 15x^2 - 12x \)[/tex] is:
[tex]\[ \boxed{3x} \][/tex]
