We appreciate your visit to Find the greatest common factor of these three expressions 10x 5 35x 4 text and 30. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Sure, let's find the greatest common factor (GCF) of the three expressions: [tex]\(10x^5\)[/tex], [tex]\(35x^4\)[/tex], and [tex]\(30\)[/tex].
### Step-by-Step Solution:
1. List the factors of each term:
- For [tex]\(10x^5\)[/tex]:
- The numeric part [tex]\(10\)[/tex] factors into [tex]\(2 \times 5\)[/tex].
- The variable part is [tex]\(x^5\)[/tex].
- So, the factors are [tex]\(2, 5,\)[/tex] and [tex]\(x^5\)[/tex].
- For [tex]\(35x^4\)[/tex]:
- The numeric part [tex]\(35\)[/tex] factors into [tex]\(5 \times 7\)[/tex].
- The variable part is [tex]\(x^4\)[/tex].
- So, the factors are [tex]\(5, 7,\)[/tex] and [tex]\(x^4\)[/tex].
- For [tex]\(30\)[/tex]:
- The numeric part [tex]\(30\)[/tex] factors into [tex]\(2 \times 3 \times 5\)[/tex].
- It does not have a variable part.
- So, the factors are [tex]\(2, 3,\)[/tex] and [tex]\(5\)[/tex].
2. Find the common numeric factors:
- The common numeric factors among [tex]\(10\)[/tex], [tex]\(35\)[/tex], and [tex]\(30\)[/tex] are examined:
- All three terms share the factor [tex]\(5\)[/tex].
3. Find the common variable factors:
- The common variable factor among [tex]\(10x^5\)[/tex], [tex]\(35x^4\)[/tex], and [tex]\(30\)[/tex] needs to be considered:
- [tex]\(10x^5\)[/tex] has [tex]\(x^5\)[/tex].
- [tex]\(35x^4\)[/tex] has [tex]\(x^4\)[/tex].
- [tex]\(30\)[/tex] does not have any [tex]\(x\)[/tex] term.
- Since [tex]\(30\)[/tex] does not have the variable [tex]\(x\)[/tex], there is no common variable factor [tex]\(x\)[/tex] among all three terms.
4. Combine the common factors:
- The numeric common factor is [tex]\(5\)[/tex].
- There are no variable factors [tex]\(x\)[/tex] common in all three terms.
### Conclusion:
The greatest common factor (GCF) of the expressions [tex]\(10x^5\)[/tex], [tex]\(35x^4\)[/tex], and [tex]\(30\)[/tex] is:
[tex]\[ \boxed{5} \][/tex]
No [tex]\(x\)[/tex] term is included in the GCF because the term [tex]\(30\)[/tex] does not have an [tex]\(x\)[/tex] in it.
### Step-by-Step Solution:
1. List the factors of each term:
- For [tex]\(10x^5\)[/tex]:
- The numeric part [tex]\(10\)[/tex] factors into [tex]\(2 \times 5\)[/tex].
- The variable part is [tex]\(x^5\)[/tex].
- So, the factors are [tex]\(2, 5,\)[/tex] and [tex]\(x^5\)[/tex].
- For [tex]\(35x^4\)[/tex]:
- The numeric part [tex]\(35\)[/tex] factors into [tex]\(5 \times 7\)[/tex].
- The variable part is [tex]\(x^4\)[/tex].
- So, the factors are [tex]\(5, 7,\)[/tex] and [tex]\(x^4\)[/tex].
- For [tex]\(30\)[/tex]:
- The numeric part [tex]\(30\)[/tex] factors into [tex]\(2 \times 3 \times 5\)[/tex].
- It does not have a variable part.
- So, the factors are [tex]\(2, 3,\)[/tex] and [tex]\(5\)[/tex].
2. Find the common numeric factors:
- The common numeric factors among [tex]\(10\)[/tex], [tex]\(35\)[/tex], and [tex]\(30\)[/tex] are examined:
- All three terms share the factor [tex]\(5\)[/tex].
3. Find the common variable factors:
- The common variable factor among [tex]\(10x^5\)[/tex], [tex]\(35x^4\)[/tex], and [tex]\(30\)[/tex] needs to be considered:
- [tex]\(10x^5\)[/tex] has [tex]\(x^5\)[/tex].
- [tex]\(35x^4\)[/tex] has [tex]\(x^4\)[/tex].
- [tex]\(30\)[/tex] does not have any [tex]\(x\)[/tex] term.
- Since [tex]\(30\)[/tex] does not have the variable [tex]\(x\)[/tex], there is no common variable factor [tex]\(x\)[/tex] among all three terms.
4. Combine the common factors:
- The numeric common factor is [tex]\(5\)[/tex].
- There are no variable factors [tex]\(x\)[/tex] common in all three terms.
### Conclusion:
The greatest common factor (GCF) of the expressions [tex]\(10x^5\)[/tex], [tex]\(35x^4\)[/tex], and [tex]\(30\)[/tex] is:
[tex]\[ \boxed{5} \][/tex]
No [tex]\(x\)[/tex] term is included in the GCF because the term [tex]\(30\)[/tex] does not have an [tex]\(x\)[/tex] in it.
Thanks for taking the time to read Find the greatest common factor of these three expressions 10x 5 35x 4 text and 30. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
