Find the Common Factor in 5z+5: Basic Algebraic Factoring

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

A common factor must appear in every term. Since z only appears in $ 5z $ but not in the constant term 5, it cannot be factored out of both terms.

Q: How do I know when I've found the greatest common factor?

The greatest common factor (GCF) is the largest number that divides all terms. In $ 5z+5 $, both terms are divisible by 5, and no larger number works for both.

Q: What if there really is no common factor?

Some expressions like $ 3x + 7y $ truly have no common factor other than 1. But always check carefully - many expressions that look unfactorable actually have hidden common factors!

Q: Can I factor out a negative number?

Yes! If you have $ -3x - 6 $, you can factor out -3 to get $ -3(x + 2) $. This is especially helpful when the leading coefficient is negative.

Q: How does factoring help me solve equations?

Factoring is the first step in solving many equations! Once you factor $ 5z + 5 = 0 $ into $ 5(z + 1) = 0 $, you can easily see that $ z = -1 $.

Factoring Algebraic Expressions with Common Terms

The expression $5z+5$

We factored into basic terms:

$5\cdot z+5$

What is the common factor of the terms?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The expression $5z+5$

We factored into basic terms:

$5\cdot z+5$

What is the common factor of the terms?

Step-by-step solution

To find the common factor of the expression $5z+5$ , we need to factor each term. The expression can be rewritten as:

$5\cdot z + 5\cdot 1$

The number 5 is common in both terms, as we can see: $\orange 5\cdot z + \orange5\cdot 1$ .

Hence, the common factor is $5$ .

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

Definition: A common factor divides evenly into all terms
Technique: Rewrite $5z+5$ as $5 \cdot z + 5 \cdot 1$
Check: Factor out 5: $5(z+1)$ expands back to $5z+5$ ✓

Common Mistakes

Avoid these frequent errors

Confusing variables with common factors
Don't choose z as the common factor just because it appears in one term = missing the actual factor! The variable z only appears in the first term, not both. Always look for numbers or variables that appear in every single term.

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

Why isn't z the common factor if it's in the expression?

A common factor must appear in every term. Since z only appears in $5z$ but not in the constant term 5, it cannot be factored out of both terms.

How do I know when I've found the greatest common factor?

The greatest common factor (GCF) is the largest number that divides all terms. In $5z+5$ , both terms are divisible by 5, and no larger number works for both.

What if there really is no common factor?

Some expressions like $3x + 7y$ truly have no common factor other than 1. But always check carefully - many expressions that look unfactorable actually have hidden common factors!

Can I factor out a negative number?

Yes! If you have $-3x - 6$ , you can factor out -3 to get $-3(x + 2)$ . This is especially helpful when the leading coefficient is negative.

How does factoring help me solve equations?

Factoring is the first step in solving many equations! Once you factor $5z + 5 = 0$ into $5(z + 1) = 0$ , you can easily see that $z = -1$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Algebraic Technique questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime