Finding Common Factors in 4x² + 16x: Step-by-Step Solution

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

Look at both the numbers and variables separately! For $ 4x^2 + 16x $, the GCF of numbers 4 and 16 is 4, and the GCF of $ x^2 $ and $ x $ is $ x $. So the overall GCF is $ 4x $.

Q: What if I factor out the wrong common factor?

No worries! You can always check your work by distributing back. If you get the original expression, you're correct. If not, look for more factors you can pull out.

Q: Can I factor out x² from both terms?

No! You can only factor out $ x^2 $ from $ 4x^2 $, but not from $ 16x $ (which only has one x). Always use the lowest power of each variable that appears in all terms.

Q: Why can't the answer be x(4x + 16)?

While this is partially factored, it's not completely factored! Notice that inside the parentheses, both terms still share a common factor of 4. The complete answer is $ 4x(x + 4) $.

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

You're done when there are no more common factors among the terms inside the parentheses. In $ 4x(x + 4) $, the terms x and 4 share no common factors besides 1.

Polynomial Factoring with Greatest Common Factor

We factored the expression

$4x^2 + 16x$

into its basic terms:

$4 \cdot x \cdot x + 16 \cdot x$

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

$4x^2 + 16x$

into its basic terms:

$4 \cdot x \cdot x + 16 \cdot x$

Take out the common factor from the factored expression

Step-by-step solution

To factor the expression $4x^2 + 16x$ , we start by identifying the greatest common factor (GCF) of $4x^2$ and $16x$ . The GCF is $4x$ . We factor out $4x$ from each term:

$4x^2+16x=\blue4\cdot \orange x\cdot x+\blue4\cdot4\cdot \orange x$ .

This simplifies the expression to $4x(x + 4)$ .

Final Answer

$4x(x + 4)$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the GCF of all terms before factoring
Technique: For $4x^2 + 16x$ , GCF is $4x$
Check: Distribute back: $4x(x + 4) = 4x^2 + 16x$ ✓

Common Mistakes

Avoid these frequent errors

Factoring out only partial common factors
Don't factor out just 4 or just x from $4x^2 + 16x$ = incomplete factoring! This leaves more common factors inside the parentheses that should be removed. Always find the greatest common factor (GCF) of all terms first.

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 of algebraic terms?

Look at both the numbers and variables separately! For $4x^2 + 16x$ , the GCF of numbers 4 and 16 is 4, and the GCF of $x^2$ and $x$ is $x$ . So the overall GCF is $4x$ .

What if I factor out the wrong common factor?

No worries! You can always check your work by distributing back. If you get the original expression, you're correct. If not, look for more factors you can pull out.

Can I factor out x² from both terms?

No! You can only factor out $x^2$ from $4x^2$ , but not from $16x$ (which only has one x). Always use the lowest power of each variable that appears in all terms.

Why can't the answer be x(4x + 16)?

While this is partially factored, it's not completely factored! Notice that inside the parentheses, both terms still share a common factor of 4. The complete answer is $4x(x + 4)$ .

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

You're done when there are no more common factors among the terms inside the parentheses. In $4x(x + 4)$ , the terms x and 4 share no common factors besides 1.

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