Factor the Expression: Breaking Down 4y² + 2y Step by Step

Q: How do I find the greatest common factor?

Look at each term separately: $ 4y^2 = 2^2 \cdot y^2 $ and $ 2y = 2 \cdot y $. The GCF includes the smallest power of each common element: 2 and y.

Q: Can I factor this expression differently?

No! When factoring completely, there's only one correct answer (ignoring order). $ 2y(2y + 1) $ is the only way to factor $ 4y^2 + 2y $ completely.

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

You're done when no more common factors can be pulled out. In $ 2y(2y + 1) $, the terms 2y and 1 inside the parentheses share no common factors except 1.

Polynomial Factoring with Common Factors

Factor the expression completely:

$4y^2 + 2y$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Factor the expression completely:

$4y^2 + 2y$

Step-by-step solution

To factor the expression $4y^2 + 2y$ , we identify the common factor in both terms:

The term $4y^2$ can be written as $2y \cdot 2y$ .

The term $2y$ can be written as $2 \cdot y$ .

The common factor is $2y$ .

Factorizing gives $2y \cdot (2y + 1)$ .

Final Answer

$2y \cdot (2y + 1)$

Key Points to Remember

Essential concepts to master this topic

Rule: Identify the greatest common factor of all terms first
Technique: Factor out 2y from $4y^2 + 2y$ to get $2y(2y + 1)$
Check: Distribute back: $2y \cdot 2y + 2y \cdot 1 = 4y^2 + 2y$ ✓

Common Mistakes

Avoid these frequent errors

Only factoring out part of the common factor
Don't factor out just 2 from $4y^2 + 2y$ = $2(2y^2 + y)$ ! This isn't completely factored because y is still common in the parentheses. Always identify the greatest common factor (GCF) which includes all common variables and their highest powers.

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 separately: $4y^2 = 2^2 \cdot y^2$ and $2y = 2 \cdot y$ . The GCF includes the smallest power of each common element: 2 and y.

What if I can't see any common factors?

Start by listing the factors of each coefficient and variable separately. For $4y^2$ : factors are 1, 2, 4, y, y². For $2y$ : factors are 1, 2, y. The common ones are 1, 2, and y.

Can I factor this expression differently?

No! When factoring completely, there's only one correct answer (ignoring order). $2y(2y + 1)$ is the only way to factor $4y^2 + 2y$ completely.

How do I know when I'm done factoring?

You're done when no more common factors can be pulled out. In $2y(2y + 1)$ , the terms 2y and 1 inside the parentheses share no common factors except 1.

Why is factoring important?

Factoring helps solve equations, simplify expressions, and find zeros of functions. It's like breaking down complex expressions into simpler building blocks that are easier to work with!

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