Answer :
To find the Greatest Common Factor (GCF) of the terms [tex]\(175x^6\)[/tex], [tex]\(-35x^7\)[/tex], and [tex]\(7x^8\)[/tex], follow these steps:
1. Find the GCF of the coefficients:
- The coefficients are 175, -35, and 7.
- Calculate the GCF of these numbers.
- The factors of 175 are: [tex]\(1, 5, 7, 25, 35, 175\)[/tex]
- The factors of -35 are: [tex]\(-1, -5, -7, -35\)[/tex]
- The factors of 7 are: [tex]\(1, 7\)[/tex]
- The common factors in all these lists are: 1 and 7
- Hence, the GCF of the coefficients is 7.
2. Determine the smallest power of [tex]\(x\)[/tex]:
- The powers of [tex]\(x\)[/tex] in the terms are 6, 7, and 8 respectively.
- The smallest of these powers is 6.
3. Combine the results:
- The GCF of the given terms will be the product of the GCF of the coefficients and [tex]\(x\)[/tex] raised to the smallest power.
- So, the GCF is [tex]\(7x^6\)[/tex].
Therefore, the GCF for the list [tex]\(175x^6, -35x^7, 7x^8\)[/tex] is [tex]\( \boxed{7x^6} \)[/tex].
1. Find the GCF of the coefficients:
- The coefficients are 175, -35, and 7.
- Calculate the GCF of these numbers.
- The factors of 175 are: [tex]\(1, 5, 7, 25, 35, 175\)[/tex]
- The factors of -35 are: [tex]\(-1, -5, -7, -35\)[/tex]
- The factors of 7 are: [tex]\(1, 7\)[/tex]
- The common factors in all these lists are: 1 and 7
- Hence, the GCF of the coefficients is 7.
2. Determine the smallest power of [tex]\(x\)[/tex]:
- The powers of [tex]\(x\)[/tex] in the terms are 6, 7, and 8 respectively.
- The smallest of these powers is 6.
3. Combine the results:
- The GCF of the given terms will be the product of the GCF of the coefficients and [tex]\(x\)[/tex] raised to the smallest power.
- So, the GCF is [tex]\(7x^6\)[/tex].
Therefore, the GCF for the list [tex]\(175x^6, -35x^7, 7x^8\)[/tex] is [tex]\( \boxed{7x^6} \)[/tex].
