Find the Common Factor in 2x²+7x: Step-by-Step Factorization

Q: How do I identify the greatest common factor?

Look at each term and find what they all share. In $ 2x^2 + 7x $, both terms have the variable x, so x is your common factor!

Q: What if there's no common factor between the numbers?

That's okay! In $ 2x^2 + 7x $, the numbers 2 and 7 don't share a common factor, but both terms still have x as a variable factor.

Q: Can I factor out more than just x?

Only if it's truly common to all terms. Here, $ 2x^2 $ has $ x^2 $ but $ 7x $ only has $ x $, so you can only factor out x.

Q: How do I know my factoring is correct?

Use the distributive property to expand your answer. If you get back to the original expression, you factored correctly!

Q: What does 'greatest common factor' mean?

It's the largest factor that divides evenly into all terms. Don't just find any common factor - find the greatest one to fully simplify the expression.

Polynomial Factoring with Common Variable Factors

The expression $2x^2+7x$ is factorised into its basic terms:

$2\cdot x\cdot x+7\cdot x$

Take out the common factor from the factorised expression.

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The expression $2x^2+7x$ is factorised into its basic terms:

$2\cdot x\cdot x+7\cdot x$

Take out the common factor from the factorised expression.

Step-by-step solution

To solve this problem, we'll focus on finding the greatest common factor of the expression $2x^2 + 7x$ .

Step 1: Identify the given expression $2x^2 + 7x$ .
Step 2: Look for common factors:
- In the term $2x^2$ , the factors are $2$ , $x$ , and $x$ .
- In the term $7x$ , the factors are $7$ and $x$ .
Step 3: Notice that the common factor here is $x$ , as it is present in both terms.
Step 4: Factor $x$ out of each term in the expression:
$2x^2 + 7x = x(2x) + x(7) = x(2x + 7)$

Therefore, the expression $2x^2 + 7x$ can be factorized as $x(2x + 7)$ .

This corresponds to choice 3, which is $x(2 \cdot x + 7)$ .

The factorized expression is $x(2x + 7)$ .

Final Answer

$x\left(2\cdot x+7\right)$

Key Points to Remember

Essential concepts to master this topic

Rule: Look for variables or coefficients present in all terms
Technique: Factor out x from $2x^2 + 7x$ gives $x(2x + 7)$
Check: Distribute back: $x \cdot 2x + x \cdot 7 = 2x^2 + 7x$ ✓

Common Mistakes

Avoid these frequent errors

Factoring out incorrect common factors
Don't factor out 2 from $2x^2 + 7x$ = $2(x^2 + 3.5x)$ ! Since 7 isn't divisible by 2, you can't factor out 2 from both terms. Always check that your common factor divides evenly into ALL terms.

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 identify the greatest common factor?

Look at each term and find what they all share. In $2x^2 + 7x$ , both terms have the variable x, so x is your common factor!

What if there's no common factor between the numbers?

That's okay! In $2x^2 + 7x$ , the numbers 2 and 7 don't share a common factor, but both terms still have x as a variable factor.

Can I factor out more than just x?

Only if it's truly common to all terms. Here, $2x^2$ has $x^2$ but $7x$ only has $x$ , so you can only factor out x.

How do I know my factoring is correct?

Use the distributive property to expand your answer. If you get back to the original expression, you factored correctly!

What does 'greatest common factor' mean?

It's the largest factor that divides evenly into all terms. Don't just find any common factor - find the greatest one to fully simplify the expression.

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