Factor the Expression 3x²+x: Finding the Common Term

Q: How do I find the greatest common factor?

Look at each term and find what they all share in common. In $ 3x^2 + x $, both terms contain x, so x is the GCF. The first term has 3·x·x and the second has 1·x.

Q: What if one term is just x?

That's fine! The term x can be written as $ 1 \cdot x $. When you factor out x, you're left with 1 inside the parentheses, giving you $ x(3x + 1) $.

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

Use the distributive property to expand your answer. If $ x(3x + 1) = 3x^2 + x $, then your factoring is correct!

Factoring Polynomials with Greatest Common Factor

We factored the expression

$3x^2+x$

into its basic terms:

$3\cdot x\cdot x+x$

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

$3x^2+x$

into its basic terms:

$3\cdot x\cdot x+x$

Take out the common factor from the factored expression

Step-by-step solution

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

Step 1: Identify the common factor
Step 2: Extract the common factor from the expression

Now, let's work through each step:
Step 1: Look at each term of the expression $3x^2 + x$ . - The term $3x^2$ can be written as $3 \cdot x \cdot x$ , and the term $x$ as $1 \cdot x$ .
From both terms, $x$ is a factor, making it the greatest common factor (GCF).

Step 2: Factor out the GCF:
Rewriting the original expression by factoring out $x$ , we have:

$x(3 \cdot x + 1)$

Therefore, the expression $3x^2 + x$ can be factored as $x(3 \cdot x + 1)$ .

This corresponds to choice 4: $x(3 \cdot x + 1)$ .

Final Answer

$x\left(3\cdot x+1\right)$

Key Points to Remember

Essential concepts to master this topic

Rule: Identify the greatest common factor shared by all terms
Technique: From $3x^2 + x$ , factor out x to get x(3x + 1)
Check: Expand x(3x + 1) = 3x² + x to verify factoring ✓

Common Mistakes

Avoid these frequent errors

Taking out only part of the common factor
Don't take out just x from 3x² and leave the second term as x = x(3x) + x! This doesn't factor completely and leaves terms outside parentheses. Always factor out the GCF from every single term in the expression.

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 find the greatest common factor?

Look at each term and find what they all share in common. In $3x^2 + x$ , both terms contain x, so x is the GCF. The first term has 3·x·x and the second has 1·x.

What if one term is just x?

That's fine! The term x can be written as $1 \cdot x$ . When you factor out x, you're left with 1 inside the parentheses, giving you $x(3x + 1)$ .

How do I check if my factoring is correct?

Use the distributive property to expand your answer. If $x(3x + 1) = 3x^2 + x$ , then your factoring is correct!

Why is x(3·x + 1) the same as x(3x + 1)?

The multiplication symbol (·) and no symbol mean the same thing in algebra. So $3 \cdot x = 3x$ . Both forms are correct!

What if there's no common factor?

If terms share no common factors other than 1, then the expression cannot be factored further using this method. You'd need other factoring techniques like grouping or special patterns.

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