Find the Common Factor in 7x + 14: Step-by-Step Factor Analysis

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

x is only in the first term! The expression $ 7x + 14 $ has x in 7x but not in 14. A common factor must appear in every single term.

Q: How do I know 7 is the greatest common factor?

Check what divides both 7 and 14: 7 ÷ 7 = 1 and 14 ÷ 7 = 2. Since 7 is the largest number that divides both coefficients evenly, it's the GCF!

Q: What if I said 14 was the common factor?

That won't work because 14 doesn't divide into 7x. You can't write 7x as 14 times something whole. Always check that your factor divides all terms evenly.

Q: Can I factor out 1 instead?

Technically yes, but that's not helpful! $ 1(7x + 14) $ doesn't simplify the expression. We want the greatest common factor to make the expression as simple as possible.

Q: How do I write the final factored form?

Once you identify 7 as the common factor, write: $ 7x + 14 = 7(x + 2) $. The numbers inside the parentheses are what's left after dividing each term by 7.

Factoring Expressions with Common Numerical Factors

The expression $7x + 14$ can be factored into basic terms:

$7 \cdot x + 7 \cdot 2$

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 $7x + 14$ can be factored into basic terms:

$7 \cdot x + 7 \cdot 2$

What is the common factor of the terms?

Step-by-step solution

To find the common factor of the expression $7x + 14$ , we need to look at the coefficients and constants.

The expression $7x + 14$ can be rewritten as $7 \cdot x + 7 \cdot 2$ .

This shows that each term contains the factor $7$ , as both terms contains it: $\orange 7 \cdot x + \orange 7 \cdot 2$ .

Therefore, the common factor is $7$ .

Final Answer

$7$

Key Points to Remember

Essential concepts to master this topic

Rule: Look for the greatest number that divides all terms
Technique: Rewrite 7x + 14 as 7(x) + 7(2)
Check: Expand factored form: 7(x + 2) = 7x + 14 ✓

Common Mistakes

Avoid these frequent errors

Choosing x as the common factor
Don't choose x as the common factor just because it appears in one term = x doesn't divide into 14! Only numerical factors that divide all terms can be factored out. Always identify the greatest number that divides every coefficient and constant.

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 both terms?

x is only in the first term! The expression $7x + 14$ has x in 7x but not in 14. A common factor must appear in every single term.

How do I know 7 is the greatest common factor?

Check what divides both 7 and 14: 7 ÷ 7 = 1 and 14 ÷ 7 = 2. Since 7 is the largest number that divides both coefficients evenly, it's the GCF!

What if I said 14 was the common factor?

That won't work because 14 doesn't divide into 7x. You can't write 7x as 14 times something whole. Always check that your factor divides all terms evenly.

Can I factor out 1 instead?

Technically yes, but that's not helpful! $1(7x + 14)$ doesn't simplify the expression. We want the greatest common factor to make the expression as simple as possible.

How do I write the final factored form?

Once you identify 7 as the common factor, write: $7x + 14 = 7(x + 2)$ . The numbers inside the parentheses are what's left after dividing each term by 7.

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