Find the Common Factor in 3x+3: Breaking Down Terms

Q: Why isn't x a common factor?

The variable x only appears in the first term $ 3x $, not in the second term $ 3 $. A common factor must divide all terms evenly.

Q: How do I know 3 divides into both terms?

Check each term: $ 3x ÷ 3 = x $ and $ 3 ÷ 3 = 1 $. Since both divisions give whole results, 3 is indeed a common factor!

Q: What if there were no common factors?

Sometimes expressions like $ 2x + 5 $ have no common factors other than 1. That's okay! Just state that 1 is the only common factor or that the terms are relatively prime.

Q: What's the difference between a factor and a term?

Terms are parts of an expression separated by + or - signsFactors are numbers or variables that multiply together to make a termIn $ 3x + 3 $, the terms are $ 3x $ and $ 3 $.

Common Factors with Simple Expressions

The expression $3x+3$ is broken down into basic terms:

$3\cdot x+3$

What is the common factor of the terms?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The expression $3x+3$ is broken down into basic terms:

$3\cdot x+3$

What is the common factor of the terms?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Break down each term of the expression $3x + 3$ .
Step 2: Identify the factors of each term.
Step 3: Determine the common factor shared by the terms.

Now, let's work through each step:
Step 1: The given expression is $3x + 3$ . It can be separated into two terms: $3x$ and $3$ .
Step 2: Breaking each term into factors, we have:

The term $3x$ can be factored as $3 \cdot x$ .
The term $3$ can be considered as $3 \cdot 1$ .

Step 3: Now, identify the common factor:

The common factor shared by the terms $3x$ and $3$ is $3$ .

Therefore, the common factor of the terms in the expression

3x + 3

is $3$ .

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Definition: Common factor divides evenly into all terms
Method: Factor each term: $3x = 3 \cdot x$ , $3 = 3 \cdot 1$
Check: Factor out 3: $3x + 3 = 3(x + 1)$ ✓

Common Mistakes

Avoid these frequent errors

Confusing common factor with largest term
Don't pick 3x as the common factor just because it's the biggest term = wrong answer! The variable x is only in one term, not both. Always look for factors that appear in every single term.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

$$ 2x^2 $$

FAQ

Everything you need to know about this question

Why isn't x a common factor?

The variable x only appears in the first term $3x$ , not in the second term $3$ . A common factor must divide all terms evenly.

How do I know 3 divides into both terms?

Check each term: $3x ÷ 3 = x$ and $3 ÷ 3 = 1$ . Since both divisions give whole results, 3 is indeed a common factor!

What if there were no common factors?

Sometimes expressions like $2x + 5$ have no common factors other than 1. That's okay! Just state that 1 is the only common factor or that the terms are relatively prime.

Can I factor out the common factor?

Absolutely! Once you find the common factor 3, you can write: $3x + 3 = 3(x + 1)$ . This is called factoring out the common factor.

What's the difference between a factor and a term?

Terms are parts of an expression separated by + or - signs
Factors are numbers or variables that multiply together to make a term

In $3x + 3$ , the terms are $3x$ and $3$ .

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