Find the Common Factor in 2ax+3x: Algebraic Expression Simplification

Q: How do I know what the common factor is?

Look for variables or numbers that appear in every single term. In $ 2ax + 3x $, both terms have x, so x is your common factor!

Q: What if there are multiple variables in some terms?

Only factor out variables that appear in all terms. Since 2ax has both a and x, but 3x only has x, you can only factor out x, not a.

Q: Can I factor out numbers too?

Yes! But only if the number divides evenly into all coefficients. Here, 2 and 3 have no common factor other than 1, so we can't factor out any numbers.

Q: How do I check if my factoring is correct?

Use the distributive property to multiply back out. If you get the original expression, you're right! $ x(2a + 3) = x \cdot 2a + x \cdot 3 = 2ax + 3x $ ✓

Q: What if I can't find any common factors?

Then the expression is already in its simplest form! Not every expression can be factored further. But in this case, x definitely appears in both terms.

Algebraic Factoring with Variable Terms

Find the common factor:

$2ax+3x$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Take out common factor

00:05 Mark the common factors

00:10 Extract the common factors from parentheses

00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the common factor:

$2ax+3x$

Step-by-step solution

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

Step 1: Identify any common factors in the terms provided.
Step 2: Factor the expression by extracting the common factor.

Now, let's work through each step:
Step 1: The expression given is $2ax + 3x$ . We observe that both terms have a common factor of $x$ .
Step 2: We factor out $x$ from each term, which results in $x(2a + 3)$ , because:

$2ax$ divided by $x$ results in $2a$ .
$3x$ divided by $x$ results in $3$ .

Therefore, the expression $2ax + 3x$ can be factored as $x(2a+3)$ .

Final Answer

$x(2a+3)$

Key Points to Remember

Essential concepts to master this topic

Common Factor Rule: Find the variable or number present in all terms
Factor Extraction: For $2ax + 3x$ , extract x to get $x(2a + 3)$
Verification Check: Multiply back: $x \cdot 2a + x \cdot 3 = 2ax + 3x$ ✓

Common Mistakes

Avoid these frequent errors

Factoring out only part of a common factor
Don't factor out just the coefficient like 3 from $2ax + 3x$ = $3(\frac{2ax}{3} + x)$ ! This creates messy fractions and isn't the greatest common factor. Always look for the complete variable factor x that appears in every term.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

$$ 4x^2 + 6x $$

FAQ

Everything you need to know about this question

How do I know what the common factor is?

Look for variables or numbers that appear in every single term. In $2ax + 3x$ , both terms have x, so x is your common factor!

What if there are multiple variables in some terms?

Only factor out variables that appear in all terms. Since 2ax has both a and x, but 3x only has x, you can only factor out x, not a.

Can I factor out numbers too?

Yes! But only if the number divides evenly into all coefficients. Here, 2 and 3 have no common factor other than 1, so we can't factor out any numbers.

How do I check if my factoring is correct?

Use the distributive property to multiply back out. If you get the original expression, you're right! $x(2a + 3) = x \cdot 2a + x \cdot 3 = 2ax + 3x$ ✓

What if I can't find any common factors?

Then the expression is already in its simplest form! Not every expression can be factored further. But in this case, x definitely appears in both terms.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Algebraic Technique questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime