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Answer :
Sure, I'd be happy to help! Let's find the greatest common factor (GCF) of [tex]\(14x^4\)[/tex] and [tex]\(9x^3\)[/tex].
### Step-by-Step Solution
1. Identify the numerical coefficients:
- First, look at the numerical parts of the expressions. Here, the coefficients are 14 and 9.
- The GCF of the numbers 14 and 9 is determined by finding the highest number that divides both 14 and 9 without leaving a remainder.
2. Finding the GCF of the numerical coefficients:
- 14 can be factored into [tex]\(2 \times 7\)[/tex].
- 9 can be factored into [tex]\(3 \times 3\)[/tex].
- Since 14 and 9 have no common factors other than 1, the GCF of 14 and 9 is 1.
3. Identify the variable parts and their exponents:
- For [tex]\(14x^4\)[/tex], the variable part is [tex]\(x^4\)[/tex].
- For [tex]\(9x^3\)[/tex], the variable part is [tex]\(x^3\)[/tex].
4. Finding the GCF of the variable parts:
- To find the GCF of [tex]\(x^4\)[/tex] and [tex]\(x^3\)[/tex], we take the variable [tex]\(x\)[/tex] to the lowest power common to both terms.
- The lowest power of [tex]\(x\)[/tex] in [tex]\(x^4\)[/tex] and [tex]\(x^3\)[/tex] is [tex]\(x^3\)[/tex].
5. Combine the GCFs of the numerical and variable parts:
- The numerical GCF is 1 (from step 2).
- The variable GCF is [tex]\(x^3\)[/tex] (from step 4).
6. Write the final GCF:
- The greatest common factor of [tex]\(14x^4\)[/tex] and [tex]\(9x^3\)[/tex] is [tex]\(1 \cdot x^3\)[/tex].
So, the GCF of [tex]\(14x^4\)[/tex] and [tex]\(9x^3\)[/tex] is [tex]\(\mathbf{x^3}\)[/tex].
I hope this helps! If you have any more questions or need further clarification, feel free to ask!
### Step-by-Step Solution
1. Identify the numerical coefficients:
- First, look at the numerical parts of the expressions. Here, the coefficients are 14 and 9.
- The GCF of the numbers 14 and 9 is determined by finding the highest number that divides both 14 and 9 without leaving a remainder.
2. Finding the GCF of the numerical coefficients:
- 14 can be factored into [tex]\(2 \times 7\)[/tex].
- 9 can be factored into [tex]\(3 \times 3\)[/tex].
- Since 14 and 9 have no common factors other than 1, the GCF of 14 and 9 is 1.
3. Identify the variable parts and their exponents:
- For [tex]\(14x^4\)[/tex], the variable part is [tex]\(x^4\)[/tex].
- For [tex]\(9x^3\)[/tex], the variable part is [tex]\(x^3\)[/tex].
4. Finding the GCF of the variable parts:
- To find the GCF of [tex]\(x^4\)[/tex] and [tex]\(x^3\)[/tex], we take the variable [tex]\(x\)[/tex] to the lowest power common to both terms.
- The lowest power of [tex]\(x\)[/tex] in [tex]\(x^4\)[/tex] and [tex]\(x^3\)[/tex] is [tex]\(x^3\)[/tex].
5. Combine the GCFs of the numerical and variable parts:
- The numerical GCF is 1 (from step 2).
- The variable GCF is [tex]\(x^3\)[/tex] (from step 4).
6. Write the final GCF:
- The greatest common factor of [tex]\(14x^4\)[/tex] and [tex]\(9x^3\)[/tex] is [tex]\(1 \cdot x^3\)[/tex].
So, the GCF of [tex]\(14x^4\)[/tex] and [tex]\(9x^3\)[/tex] is [tex]\(\mathbf{x^3}\)[/tex].
I hope this helps! If you have any more questions or need further clarification, feel free to ask!
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