Question
Find the common factor
14x^2 - 12x
14x^2 - 12x
Answers
GPT-4o mini
To find the common factor of the expression \(14x^2 - 12x\), we can first identify the greatest common factor (GCF) of the coefficients and the variable.
1. **Coefficients:** The coefficients are 14 and 12.
- The factors of 14 are: 1, 2, 7, 14
- The factors of 12 are: 1, 2, 3, 4, 6, 12
- The greatest common factor is 2.
2. **Variable:** Both terms have the variable \(x\) in them. The lowest power of \(x\) in the expression is \(x^1\).
Combining these, the GCF of the entire expression is \(2x\).
Now, we can factor \(2x\) out of the expression:
\[
14x^2 - 12x = 2x(7x - 6)
\]
So the common factor is \(2x\).
1. **Coefficients:** The coefficients are 14 and 12.
- The factors of 14 are: 1, 2, 7, 14
- The factors of 12 are: 1, 2, 3, 4, 6, 12
- The greatest common factor is 2.
2. **Variable:** Both terms have the variable \(x\) in them. The lowest power of \(x\) in the expression is \(x^1\).
Combining these, the GCF of the entire expression is \(2x\).
Now, we can factor \(2x\) out of the expression:
\[
14x^2 - 12x = 2x(7x - 6)
\]
So the common factor is \(2x\).