Factor Out Common Terms in 5x²+10x: Step-by-Step Solution

Q: How do I find the greatest common factor of the terms?

Look at each term's coefficient and variables separately. For $ 5x^2 + 10x $: coefficients 5 and 10 share GCF of 5, variables $ x^2 $ and $ x $ share GCF of $ x $. Combine them: $ 5x $.

Q: What if I factor out the wrong amount?

You can always check by expanding your factored form! If $ 5x(x + 2) $ expands back to $ 5x^2 + 10x $, you factored correctly. If not, try again.

Q: Why can't I factor out just 5 instead of 5x?

Factoring out just 5 gives you $ 5(x^2 + 2x) $, but you can still factor more! The terms $ x^2 $ and $ 2x $ both have $ x $ in common, so $ 5x(x + 2) $ is completely factored.

Q: How do I know when I'm completely done factoring?

You're done when no common factors remain in the parentheses. In $ 5x(x + 2) $, the terms $ x $ and $ 2 $ share no common factors except 1.

Q: What if one term doesn't seem to have the common factor?

Every term must contain the common factor for it to be factored out. Double-check by writing each term in expanded form: $ 5x^2 = 5 \cdot x \cdot x $ and $ 10x = 5 \cdot 2 \cdot x $. Both contain $ 5x $!

Factoring Polynomials with Common Monomial Terms

We factored the expression

$5x^2+10x$ into its basic terms:

$5\cdot x\cdot x+5\cdot2\cdot x$

Take out the common factor from the factored expression

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

We factored the expression

$5x^2+10x$ into its basic terms:

$5\cdot x\cdot x+5\cdot2\cdot x$

Take out the common factor from the factored expression

Step-by-step solution

To factor the expression $5x^2 + 10x$ , first identify the common factor in each term. Here, both terms share a $5x$ factor.

$\blue 5\cdot \orange x\cdot x+\blue5\cdot2\cdot\orange x$

Next, factor out $5x$ from each term:

$5x^2 + 10x = 5x(x + 2)$

The common factor extracted is $5x(x + 2)$ , making it the simplified expression.

Final Answer

$5x(x + 2)$

Key Points to Remember

Essential concepts to master this topic

Rule: Identify the greatest common factor in all terms first
Technique: Factor out $5x$ from both $5x^2$ and $10x$
Check: Expand $5x(x + 2) = 5x^2 + 10x$ to verify ✓

Common Mistakes

Avoid these frequent errors

Factoring out only part of the common factor
Don't factor out just 5 or just x = incomplete factoring! This leaves extra common factors that should be removed. Always find the greatest common factor of all terms and factor it out completely.

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

How do I find the greatest common factor of the terms?

Look at each term's coefficient and variables separately. For $5x^2 + 10x$ : coefficients 5 and 10 share GCF of 5, variables $x^2$ and $x$ share GCF of $x$ . Combine them: $5x$ .

What if I factor out the wrong amount?

You can always check by expanding your factored form! If $5x(x + 2)$ expands back to $5x^2 + 10x$ , you factored correctly. If not, try again.

Why can't I factor out just 5 instead of 5x?

Factoring out just 5 gives you $5(x^2 + 2x)$ , but you can still factor more! The terms $x^2$ and $2x$ both have $x$ in common, so $5x(x + 2)$ is completely factored.

How do I know when I'm completely done factoring?

You're done when no common factors remain in the parentheses. In $5x(x + 2)$ , the terms $x$ and $2$ share no common factors except 1.

What if one term doesn't seem to have the common factor?

Every term must contain the common factor for it to be factored out. Double-check by writing each term in expanded form: $5x^2 = 5 \cdot x \cdot x$ and $10x = 5 \cdot 2 \cdot x$ . Both contain $5x$ !

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