Find the Common Factor in 5x + 10: Expression Breakdown

Q: Why isn't x the common factor if it's in the expression?

A common factor must appear in every single term. Since x only appears in $ 5x $ but not in $ 10 $, it's not common to both terms.

Q: How do I know 5 is the biggest common factor?

Check what divides both terms: 5 divides $ 5x $ and 5 divides $ 10 $. Since 10 = 5 × 2, we can't factor out anything larger than 5.

Q: What if I factored out 1 instead?

Factoring out 1 gives $ 1(5x + 10) $, which is technically correct but not simplified. Always factor out the greatest common factor to fully simplify.

Q: Can I factor this expression further after finding 5?

After factoring out 5, you get $ 5(x + 2) $. The expression $ (x + 2) $ cannot be factored further since x and 2 have no common factors.

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

Use the distributive property to multiply back: $ 5(x + 2) = 5 \cdot x + 5 \cdot 2 = 5x + 10 $. If you get the original expression, your factoring is correct!

Factoring Expressions with Numerical Coefficients

The expression $5x + 10$ can be factored into basic terms:

$5 \cdot x + 5 \cdot 2$

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 $5x + 10$ can be factored into basic terms:

$5 \cdot x + 5 \cdot 2$

What is the common factor of the terms?

Step-by-step solution

To find the common factor of the expression $5x + 10$ , we need to look at the coefficients and constants.

The expression $5x + 10$ can be rewritten as $5 \cdot x + 5 \cdot 2$ .

This shows that each term contains the factor $5$ , as we can see it shows up in both of the terms: $\orange5 \cdot x + \orange5 \cdot 2$ .

Therefore, the common factor is $5$ .

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the largest number that divides all terms evenly
Technique: Rewrite each term showing the factor: $5x = 5 \cdot x$ and $10 = 5 \cdot 2$
Check: Factor out and multiply back: $5(x + 2) = 5x + 10$ ✓

Common Mistakes

Avoid these frequent errors

Confusing the variable with the common factor
Don't think x is the common factor just because it appears in one term = wrong factoring! The variable x only appears in the first term, not in 10. Always look for numbers that divide ALL terms evenly.

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 x the common factor if it's in the expression?

A common factor must appear in every single term. Since x only appears in $5x$ but not in $10$ , it's not common to both terms.

How do I know 5 is the biggest common factor?

Check what divides both terms: 5 divides $5x$ and 5 divides $10$ . Since 10 = 5 × 2, we can't factor out anything larger than 5.

What if I factored out 1 instead?

Factoring out 1 gives $1(5x + 10)$ , which is technically correct but not simplified. Always factor out the greatest common factor to fully simplify.

Can I factor this expression further after finding 5?

After factoring out 5, you get $5(x + 2)$ . The expression $(x + 2)$ cannot be factored further since x and 2 have no common factors.

How do I check if my factoring is correct?

Use the distributive property to multiply back: $5(x + 2) = 5 \cdot x + 5 \cdot 2 = 5x + 10$ . If you get the original expression, your factoring is correct!

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