To find the Greatest Common Factor (GCF) of the expression [tex]\(36x^2 + 6x\)[/tex], we need to follow these steps:
1. Identify the Terms: The expression [tex]\(36x^2 + 6x\)[/tex] consists of two terms: [tex]\(36x^2\)[/tex] and [tex]\(6x\)[/tex].
2. Factor Each Coefficient: We start by finding the GCF of the numerical coefficients:
- The coefficient of the first term [tex]\(36x^2\)[/tex] is 36.
- The coefficient of the second term [tex]\(6x\)[/tex] is 6.
We need to determine the GCF of 36 and 6.
- The factors of 36 are: [tex]\(1, 2, 3, 4, 6, 9, 12, 18, 36\)[/tex].
- The factors of 6 are: [tex]\(1, 2, 3, 6\)[/tex].
The greatest common factor of 36 and 6 is 6.
3. Consider the Variable Part: Next, we look at the variable part [tex]\(x\)[/tex] in each term:
- The first term has [tex]\(x^2\)[/tex], and the second term has [tex]\(x\)[/tex].
The common variable part between [tex]\(x^2\)[/tex] and [tex]\(x\)[/tex] is [tex]\(x\)[/tex]. That is, the least power of [tex]\(x\)[/tex] present in both terms is [tex]\(x\)[/tex].
4. Combine the GCF of the Coefficients and the Variable Part:
- The numerical GCF is 6.
- The variable part GCF is [tex]\(x\)[/tex].
Therefore, the GCF of the entire expression [tex]\(36x^2 + 6x\)[/tex] is [tex]\(6x\)[/tex].
5. Conclusion: The Greatest Common Factor (GCF) of the expression [tex]\(36x^2 + 6x\)[/tex] is [tex]\(6x\)[/tex].
Hence, the correct answer is:
(G) [tex]\(6x\)[/tex]
