Answer :
To find the greatest common factor (GCF) of the terms [tex]\(63x^5\)[/tex], [tex]\(-21x^6\)[/tex], and [tex]\(7x^7\)[/tex], follow these steps:
1. Identify the Coefficients:
- The coefficients are 63, -21, and 7.
2. Find the GCF of the Coefficients:
- We need to find the GCF of 63, 21, and 7.
- The factors of 63 are: 1, 3, 7, 9, 21, 63.
- The factors of 21 are: 1, 3, 7, 21.
- The factors of 7 are: 1, 7.
- The largest number that appears in each set of factors is 7.
- Therefore, the GCF of 63, 21, and 7 is 7.
3. Identify the Powers of [tex]\(x\)[/tex]:
- The powers of [tex]\(x\)[/tex] in each term are 5, 6, and 7 respectively.
4. Determine the Minimum Power of [tex]\(x\)[/tex]:
- Among 5, 6, and 7, the smallest power is 5.
5. Combine the GCF of the Coefficients and the Minimum Power of [tex]\(x\)[/tex]:
- Multiply the GCF of the coefficients, which is 7, by [tex]\(x\)[/tex] raised to the minimum power, which is [tex]\(x^5\)[/tex].
Thus, the GCF of the expressions [tex]\(63x^5\)[/tex], [tex]\(-21x^6\)[/tex], and [tex]\(7x^7\)[/tex] is [tex]\(7x^5\)[/tex].
1. Identify the Coefficients:
- The coefficients are 63, -21, and 7.
2. Find the GCF of the Coefficients:
- We need to find the GCF of 63, 21, and 7.
- The factors of 63 are: 1, 3, 7, 9, 21, 63.
- The factors of 21 are: 1, 3, 7, 21.
- The factors of 7 are: 1, 7.
- The largest number that appears in each set of factors is 7.
- Therefore, the GCF of 63, 21, and 7 is 7.
3. Identify the Powers of [tex]\(x\)[/tex]:
- The powers of [tex]\(x\)[/tex] in each term are 5, 6, and 7 respectively.
4. Determine the Minimum Power of [tex]\(x\)[/tex]:
- Among 5, 6, and 7, the smallest power is 5.
5. Combine the GCF of the Coefficients and the Minimum Power of [tex]\(x\)[/tex]:
- Multiply the GCF of the coefficients, which is 7, by [tex]\(x\)[/tex] raised to the minimum power, which is [tex]\(x^5\)[/tex].
Thus, the GCF of the expressions [tex]\(63x^5\)[/tex], [tex]\(-21x^6\)[/tex], and [tex]\(7x^7\)[/tex] is [tex]\(7x^5\)[/tex].
