Simplify the Expression (5x + 10): Finding the Common Factor

Factoring Expressions with Common Coefficients

Simplify the expression 5x+10 5x + 10 by factoring it. Find the common factor.

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Step-by-step written solution

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1

Understand the problem

Simplify the expression 5x+10 5x + 10 by factoring it. Find the common factor.

2

Step-by-step solution

First, identify the coefficients and the terms in the expression 5x+10 5x + 10 .

Break down each term:

5x 5x can be written as 5x 5 \cdot x .

10 10 can be written as 52 5 \cdot 2 .

The common factor of these two terms is 5 5 .

Therefore, the factored form of the expression is 5(x+2) 5(x + 2) , and the common factor is 5 5 .

3

Final Answer

5 5

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find the greatest common factor (GCF) of all terms
  • Technique: Rewrite 5x as 5·x and 10 as 5·2
  • Check: Expand 5(x + 2) to verify it equals 5x + 10 ✓

Common Mistakes

Avoid these frequent errors
  • Choosing the wrong common factor
    Don't just pick any number that divides into both terms = incomplete factoring! For example, choosing 2 instead of 5 leaves extra factors. Always find the greatest common factor (GCF) to fully simplify.

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 if 5 is really the greatest common factor?

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Check if any larger number divides both terms! Since 5 divides 5x and 5 divides 10, and no number larger than 5 divides both, then 5 is the GCF.

What if I can't see the common factor right away?

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Break each term into its prime factors! Write 5x as 5·x and 10 as 2·5. The common factor jumps out: it's 5!

Can x be a common factor too?

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No, because x doesn't appear in the term 10. A common factor must divide every single term in the expression.

How do I check if my factoring is correct?

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Use the distributive property to expand your answer! 5(x+2)=5x+10 5(x + 2) = 5x + 10 matches the original expression, so it's correct!

What happens if there's no common factor?

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Sometimes expressions can't be factored using common factors. But in 5x+10 5x + 10 , both terms are multiples of 5, so factoring is definitely possible!

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