To find the greatest common factor (GCF) of the terms [tex]\(14 c^2 d\)[/tex] and [tex]\(42 c^3 d\)[/tex], we can break down the problem into several steps:
1. Determine the GCF of the numerical coefficients:
- The coefficients are 14 and 42.
- The Greatest Common Factor of 14 and 42 is 14.
2. Determine the GCF of the variable [tex]\(c\)[/tex]:
- The first term has [tex]\(c^2\)[/tex].
- The second term has [tex]\(c^3\)[/tex].
- The GCF is the variable raised to the lowest power present in both terms. So, for [tex]\(c\)[/tex], the GCF is [tex]\(c^2\)[/tex].
3. Determine the GCF of the variable [tex]\(d\)[/tex]:
- Both terms have [tex]\(d\)[/tex] to the power of 1.
- Since the exponent for [tex]\(d\)[/tex] is the same in both terms, the GCF is [tex]\(d\)[/tex].
Combining these factors, the GCF of [tex]\(14 c^2 d\)[/tex] and [tex]\(42 c^3 d\)[/tex] is:
[tex]\[ 14 c^2 d \][/tex]
So, the correct choice is:
[tex]\[
\boxed{14 c^2 d}
\][/tex]
