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Answer :
To find the greatest common factor (GCF) of [tex]\(3x^4\)[/tex], [tex]\(15x^3\)[/tex], and [tex]\(21x^2\)[/tex], follow these steps:
1. Identify the Coefficients: Look at the numerical part of each term:
- The coefficients are 3, 15, and 21.
2. Determine the GCF of the Coefficients:
- List the factors:
- Factors of 3: 1, 3
- Factors of 15: 1, 3, 5, 15
- Factors of 21: 1, 3, 7, 21
- The greatest common factor of these numbers is 3.
3. Examine the Variable Parts:
- The terms all contain the variable [tex]\(x\)[/tex].
- The exponents of [tex]\(x\)[/tex] in the expressions are 4, 3, and 2.
4. Find the Smallest Power of [tex]\(x\)[/tex]:
- The smallest power among [tex]\(x^4\)[/tex], [tex]\(x^3\)[/tex], and [tex]\(x^2\)[/tex] is [tex]\(x^2\)[/tex].
5. Combine the GCF of the Coefficients and the Smallest Power of the Variable:
- Multiply the GCF of the coefficients (3) by the smallest power of the variable, which is [tex]\(x^2\)[/tex].
Therefore, the greatest common factor of [tex]\(3x^4\)[/tex], [tex]\(15x^3\)[/tex], and [tex]\(21x^2\)[/tex] is [tex]\(3x^2\)[/tex].
1. Identify the Coefficients: Look at the numerical part of each term:
- The coefficients are 3, 15, and 21.
2. Determine the GCF of the Coefficients:
- List the factors:
- Factors of 3: 1, 3
- Factors of 15: 1, 3, 5, 15
- Factors of 21: 1, 3, 7, 21
- The greatest common factor of these numbers is 3.
3. Examine the Variable Parts:
- The terms all contain the variable [tex]\(x\)[/tex].
- The exponents of [tex]\(x\)[/tex] in the expressions are 4, 3, and 2.
4. Find the Smallest Power of [tex]\(x\)[/tex]:
- The smallest power among [tex]\(x^4\)[/tex], [tex]\(x^3\)[/tex], and [tex]\(x^2\)[/tex] is [tex]\(x^2\)[/tex].
5. Combine the GCF of the Coefficients and the Smallest Power of the Variable:
- Multiply the GCF of the coefficients (3) by the smallest power of the variable, which is [tex]\(x^2\)[/tex].
Therefore, the greatest common factor of [tex]\(3x^4\)[/tex], [tex]\(15x^3\)[/tex], and [tex]\(21x^2\)[/tex] is [tex]\(3x^2\)[/tex].
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