Answer :
To find the Greatest Common Factor (GCF) of the terms in the expression [tex]\(45x^6 + 6x^5\)[/tex], follow these steps:
1. Identify the Coefficients and Powers of x:
The expression [tex]\(45x^6 + 6x^5\)[/tex] has two terms: [tex]\(45x^6\)[/tex] and [tex]\(6x^5\)[/tex].
- For the term [tex]\(45x^6\)[/tex], the coefficient is 45, and the power of [tex]\(x\)[/tex] is 6.
- For the term [tex]\(6x^5\)[/tex], the coefficient is 6, and the power of [tex]\(x\)[/tex] is 5.
2. Calculate the GCF of the Coefficients:
To find the GCF of the coefficients 45 and 6, list the factors of each:
- Factors of 45: 1, 3, 5, 9, 15, 45
- Factors of 6: 1, 2, 3, 6
The greatest common factor they share is 3.
3. Determine the Common Factor for the Variable [tex]\(x\)[/tex]:
Since the terms are [tex]\(x^6\)[/tex] and [tex]\(x^5\)[/tex], find the smallest power of [tex]\(x\)[/tex] that both terms have. Here, that is [tex]\(x^5\)[/tex].
4. Combine the GCF of the Coefficients with the GCF of the Variables:
Combine the greatest common factor of the coefficients (3) with the common factor of the variables (which is [tex]\(x^5\)[/tex]).
Therefore, the GCF of the expression [tex]\(45x^6 + 6x^5\)[/tex] is [tex]\(3x^5\)[/tex].
In summary, the GCF of the terms in the expression [tex]\(45x^6 + 6x^5\)[/tex] is [tex]\(3x^5\)[/tex].
1. Identify the Coefficients and Powers of x:
The expression [tex]\(45x^6 + 6x^5\)[/tex] has two terms: [tex]\(45x^6\)[/tex] and [tex]\(6x^5\)[/tex].
- For the term [tex]\(45x^6\)[/tex], the coefficient is 45, and the power of [tex]\(x\)[/tex] is 6.
- For the term [tex]\(6x^5\)[/tex], the coefficient is 6, and the power of [tex]\(x\)[/tex] is 5.
2. Calculate the GCF of the Coefficients:
To find the GCF of the coefficients 45 and 6, list the factors of each:
- Factors of 45: 1, 3, 5, 9, 15, 45
- Factors of 6: 1, 2, 3, 6
The greatest common factor they share is 3.
3. Determine the Common Factor for the Variable [tex]\(x\)[/tex]:
Since the terms are [tex]\(x^6\)[/tex] and [tex]\(x^5\)[/tex], find the smallest power of [tex]\(x\)[/tex] that both terms have. Here, that is [tex]\(x^5\)[/tex].
4. Combine the GCF of the Coefficients with the GCF of the Variables:
Combine the greatest common factor of the coefficients (3) with the common factor of the variables (which is [tex]\(x^5\)[/tex]).
Therefore, the GCF of the expression [tex]\(45x^6 + 6x^5\)[/tex] is [tex]\(3x^5\)[/tex].
In summary, the GCF of the terms in the expression [tex]\(45x^6 + 6x^5\)[/tex] is [tex]\(3x^5\)[/tex].
