Answer :
Certainly! Let's find the greatest common factor (GCF) of the expressions [tex]\(36x^4\)[/tex] and [tex]\(48x^3\)[/tex] step-by-step.
1. Identify the coefficients:
The coefficients are the numerical parts in front of the variables in each expression.
- In [tex]\(36x^4\)[/tex], the coefficient is 36.
- In [tex]\(48x^3\)[/tex], the coefficient is 48.
2. Find the GCF of the coefficients:
To find the GCF of 36 and 48, list the factors:
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The common factors are 1, 2, 3, 4, 6, and 12. The greatest of these is 12.
3. Identify the variable parts:
Both expressions have the variable [tex]\(x\)[/tex].
- In [tex]\(36x^4\)[/tex], the power of [tex]\(x\)[/tex] is 4.
- In [tex]\(48x^3\)[/tex], the power of [tex]\(x\)[/tex] is 3.
4. Find the GCF of the variable parts:
For [tex]\(x^4\)[/tex] and [tex]\(x^3\)[/tex], take the lower of the exponents. The lower power of [tex]\(x\)[/tex] is [tex]\(x^3\)[/tex].
5. Combine the GCF of the coefficients and the variable parts:
- GCF of coefficients is 12.
- GCF of variable parts is [tex]\(x^3\)[/tex].
Therefore, the GCF of [tex]\(36x^4\)[/tex] and [tex]\(48x^3\)[/tex] is [tex]\(12x^3\)[/tex].
That's the complete step-by-step process to find the GCF of the given expressions. The result is [tex]\(12x^3\)[/tex].
1. Identify the coefficients:
The coefficients are the numerical parts in front of the variables in each expression.
- In [tex]\(36x^4\)[/tex], the coefficient is 36.
- In [tex]\(48x^3\)[/tex], the coefficient is 48.
2. Find the GCF of the coefficients:
To find the GCF of 36 and 48, list the factors:
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The common factors are 1, 2, 3, 4, 6, and 12. The greatest of these is 12.
3. Identify the variable parts:
Both expressions have the variable [tex]\(x\)[/tex].
- In [tex]\(36x^4\)[/tex], the power of [tex]\(x\)[/tex] is 4.
- In [tex]\(48x^3\)[/tex], the power of [tex]\(x\)[/tex] is 3.
4. Find the GCF of the variable parts:
For [tex]\(x^4\)[/tex] and [tex]\(x^3\)[/tex], take the lower of the exponents. The lower power of [tex]\(x\)[/tex] is [tex]\(x^3\)[/tex].
5. Combine the GCF of the coefficients and the variable parts:
- GCF of coefficients is 12.
- GCF of variable parts is [tex]\(x^3\)[/tex].
Therefore, the GCF of [tex]\(36x^4\)[/tex] and [tex]\(48x^3\)[/tex] is [tex]\(12x^3\)[/tex].
That's the complete step-by-step process to find the GCF of the given expressions. The result is [tex]\(12x^3\)[/tex].
