Find the Common Factor in 4x² + 3x: Term-by-Term Analysis

Q: Why isn't 4x the greatest common factor?

While $ 4x^2 $ contains $ 4x $, the term $ 3x $ does not contain $ 4x $. The greatest common factor must be present in all terms.

Q: How do I know x is really the greatest common factor?

Check each term: $ 4x^2 = 4 \cdot x \cdot x $ contains x, and $ 3x = 3 \cdot x $ contains x. Since no larger factor appears in both terms, x is the GCF.

Q: Can I factor out more than just x?

Only if there's a larger common factor! Here, the coefficients 4 and 3 have no common factor except 1, so $ x $ is the greatest common factor we can remove.

Q: How do I verify my factoring is correct?

Multiply your factored form back out: $ x(4x + 3) = 4x^2 + 3x $. If you get the original expression, your factoring is correct!

Greatest Common Factor with Polynomial Terms

We factored the expression

$4x^2+3x$ into its basic terms:

$4\cdot x\cdot x+3\cdot x$

What common factor can be found in these terms?

❤️ Continue Your Math Journey!

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

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

We factored the expression

$4x^2+3x$ into its basic terms:

$4\cdot x\cdot x+3\cdot x$

What common factor can be found in these terms?

Step-by-step solution

First, consider the expression $4x^2+3x$ . We want to factor out the greatest common factor of the terms.

Both terms, $4x^2$ and $3x$ , contain the factor $x$ . Therefore, $x$ is a common factor.

Write each term showing the factor $x$ : $4\cdot x\cdot \orange x$ and $3\cdot \orange x$ .

The greatest common factor is $x$ .

Final Answer

$x$

Key Points to Remember

Essential concepts to master this topic

Rule: Look for variables and numbers that appear in every term
Technique: Break down $4x^2$ into $4 \cdot x \cdot x$ to see common factors
Check: Factor out x: $x(4x + 3)$ expands back to original expression ✓

Common Mistakes

Avoid these frequent errors

Choosing the coefficient as the common factor
Don't pick just the number 4 as the common factor = you'll miss the variable x! The coefficient 3 doesn't contain 4, so 4 isn't common to both terms. Always check that your chosen factor appears in every single 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

Why isn't 4x the greatest common factor?

While $4x^2$ contains $4x$ , the term $3x$ does not contain $4x$ . The greatest common factor must be present in all terms.

How do I know x is really the greatest common factor?

Check each term: $4x^2 = 4 \cdot x \cdot x$ contains x, and $3x = 3 \cdot x$ contains x. Since no larger factor appears in both terms, x is the GCF.

What if there were no common factors?

If no variables or numbers appear in all terms, then the expression cannot be factored using common factors. You'd need other factoring methods or leave it as is.

Can I factor out more than just x?

Only if there's a larger common factor! Here, the coefficients 4 and 3 have no common factor except 1, so $x$ is the greatest common factor we can remove.

How do I verify my factoring is correct?

Multiply your factored form back out: $x(4x + 3) = 4x^2 + 3x$ . If you get the original expression, your factoring is correct!

🌟 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