To find the Greatest Common Factor (GCF) of [tex]\(44 j^5 k^4\)[/tex] and [tex]\(121 j^2 k^6\)[/tex], we'll break the problem down into three steps:
1. Find the GCF of the coefficients (44 and 121):
- The factors of 44 are 1, 2, 4, 11, 22, 44.
- The factors of 121 are 1, 11, 121.
- The highest common factor between 44 and 121 is 11.
2. Find the GCF of [tex]\(j^5\)[/tex] and [tex]\(j^2\)[/tex]:
- When considering powers of the same variable, the GCF is given by the lower power.
- So, for [tex]\(j^5\)[/tex] and [tex]\(j^2\)[/tex], the GCF is [tex]\(j^2\)[/tex].
3. Find the GCF of [tex]\(k^4\)[/tex] and [tex]\(k^6\)[/tex]:
- Similarly, when considering powers of the same variable, the GCF is the lower power.
- So, for [tex]\(k^4\)[/tex] and [tex]\(k^6\)[/tex], the GCF is [tex]\(k^4\)[/tex].
Now combining these GCFs, we get:
- Coefficient GCF: 11
- Variable [tex]\(j\)[/tex] GCF: [tex]\(j^2\)[/tex]
- Variable [tex]\(k\)[/tex] GCF: [tex]\(k^4\)[/tex]
So, the GCF of [tex]\(44 j^5 k^4\)[/tex] and [tex]\(121 j^2 k^6\)[/tex] is:
[tex]\[ 11 j^2 k^4 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{11 j^2 k^4} \][/tex]
