To find the greatest common factor (GCF) of the terms [tex]\(20x^{76}\)[/tex] and [tex]\(8x^{92}\)[/tex], follow these steps:
1. Identify the coefficients:
- The coefficient of the first term is [tex]\(20\)[/tex].
- The coefficient of the second term is [tex]\(8\)[/tex].
2. Find the GCF of the coefficients:
- The factors of [tex]\(20\)[/tex] are [tex]\(1, 2, 4, 5, 10, 20\)[/tex].
- The factors of [tex]\(8\)[/tex] are [tex]\(1, 2, 4, 8\)[/tex].
- The greatest common factor of [tex]\(20\)[/tex] and [tex]\(8\)[/tex] is [tex]\(4\)[/tex].
3. Identify the exponents of [tex]\(x\)[/tex]:
- The exponent of [tex]\(x\)[/tex] in the first term is [tex]\(76\)[/tex].
- The exponent of [tex]\(x\)[/tex] in the second term is [tex]\(92\)[/tex].
4. Find the smallest exponent:
- Between [tex]\(76\)[/tex] and [tex]\(92\)[/tex], the smaller exponent is [tex]\(76\)[/tex].
5. Combine the results:
- The greatest common factor of the coefficients is [tex]\(4\)[/tex].
- The smallest exponent is [tex]\(76\)[/tex].
- Therefore, the greatest common factor of the terms [tex]\(20x^{76}\)[/tex] and [tex]\(8x^{92}\)[/tex] is [tex]\(4x^{76}\)[/tex].
The detailed solution yields [tex]\(4x^{76}\)[/tex] as the greatest common factor of [tex]\(20x^{76}\)[/tex] and [tex]\(8x^{92}\)[/tex].
