Answer :
To find the greatest common factor (GCF) of the terms [tex]\(30x^4\)[/tex], [tex]\(70x^6\)[/tex], and [tex]\(60x^9\)[/tex], we can follow these steps:
1. Identify the Coefficients:
- The coefficients of the terms are 30, 70, and 60.
2. Find the GCD of the Coefficients:
- The greatest common divisor (GCD) of 30, 70, and 60 is determined by finding the largest number that divides all three numbers evenly.
- The GCD of these coefficients is 10.
3. Determine the Smallest Power of [tex]\(x\)[/tex]:
- Look at the powers of [tex]\(x\)[/tex] in each term: [tex]\(x^4\)[/tex], [tex]\(x^6\)[/tex], and [tex]\(x^9\)[/tex].
- The smallest power of [tex]\(x\)[/tex] is [tex]\(x^4\)[/tex].
4. Combine the Results:
- The greatest common factor (GCF) is the product of the GCD of the coefficients (10) and the smallest power of [tex]\(x\)[/tex] ([tex]\(x^4\)[/tex]).
So, the greatest common factor for the list of terms [tex]\(30x^4\)[/tex], [tex]\(70x^6\)[/tex], and [tex]\(60x^9\)[/tex] is [tex]\(10x^4\)[/tex].
1. Identify the Coefficients:
- The coefficients of the terms are 30, 70, and 60.
2. Find the GCD of the Coefficients:
- The greatest common divisor (GCD) of 30, 70, and 60 is determined by finding the largest number that divides all three numbers evenly.
- The GCD of these coefficients is 10.
3. Determine the Smallest Power of [tex]\(x\)[/tex]:
- Look at the powers of [tex]\(x\)[/tex] in each term: [tex]\(x^4\)[/tex], [tex]\(x^6\)[/tex], and [tex]\(x^9\)[/tex].
- The smallest power of [tex]\(x\)[/tex] is [tex]\(x^4\)[/tex].
4. Combine the Results:
- The greatest common factor (GCF) is the product of the GCD of the coefficients (10) and the smallest power of [tex]\(x\)[/tex] ([tex]\(x^4\)[/tex]).
So, the greatest common factor for the list of terms [tex]\(30x^4\)[/tex], [tex]\(70x^6\)[/tex], and [tex]\(60x^9\)[/tex] is [tex]\(10x^4\)[/tex].
