Answer :
To find the greatest common factor (GCF) of the terms [tex]\(30x^2\)[/tex] and [tex]\(45x^5\)[/tex], we need to consider both the numerical coefficients and the variable parts separately.
1. Find the GCF of the coefficients:
- The coefficients are 30 and 45.
- To find the GCF of 30 and 45, we list the factors of each:
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 45: 1, 3, 5, 9, 15, 45
- The greatest factor common to both sets is 15.
2. Find the GCF of the variable parts:
- The variable parts are [tex]\(x^2\)[/tex] and [tex]\(x^5\)[/tex].
- Since both terms contain the variable [tex]\(x\)[/tex], we take the smallest exponent:
- In this case, it's [tex]\(x^2\)[/tex].
3. Combine the GCF of the coefficients and the variable parts:
- The GCF is the product of the greatest common factor of the coefficients (15) and the smallest power of [tex]\(x\)[/tex] that appears in both terms ([tex]\(x^2\)[/tex]).
- Therefore, the greatest common factor for [tex]\(30x^2\)[/tex] and [tex]\(45x^5\)[/tex] is [tex]\(15x^2\)[/tex].
So, the greatest common factor is [tex]\(15x^2\)[/tex].
1. Find the GCF of the coefficients:
- The coefficients are 30 and 45.
- To find the GCF of 30 and 45, we list the factors of each:
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 45: 1, 3, 5, 9, 15, 45
- The greatest factor common to both sets is 15.
2. Find the GCF of the variable parts:
- The variable parts are [tex]\(x^2\)[/tex] and [tex]\(x^5\)[/tex].
- Since both terms contain the variable [tex]\(x\)[/tex], we take the smallest exponent:
- In this case, it's [tex]\(x^2\)[/tex].
3. Combine the GCF of the coefficients and the variable parts:
- The GCF is the product of the greatest common factor of the coefficients (15) and the smallest power of [tex]\(x\)[/tex] that appears in both terms ([tex]\(x^2\)[/tex]).
- Therefore, the greatest common factor for [tex]\(30x^2\)[/tex] and [tex]\(45x^5\)[/tex] is [tex]\(15x^2\)[/tex].
So, the greatest common factor is [tex]\(15x^2\)[/tex].
