Factor the GCF out of:8x+128x+12

4 ( 2 x + 3 ) 4\left(2x+3\right)

Factor the GCF out of: 8 x + 12 8x+12

Here we have the polynomial eight x plus 12, and we want to factor it using the GCF method. So first, we need to identify what the greatest common factor is. So we're going to list out the prime factorization for each of our terms. We know that the prime factorization for eight is two times two times two, and for x is just x. And the prime factorization for 12 is two times two times three. So the factors that they have in common are two, as well as a second two, which makes our greatest common factor two times two, which is four. So now I want to rewrite each term as a product with the greatest common factor. So what can I multiply four by to get eight x? Well that would be two x. So I can rewrite eight x as four times two x. And what can I multiply four by to get 12? That's three. So I can rewrite 12 as four times three. Now I can factor out four and I'm left with two x plus three. And this here is our final answer.

Factor the GCF out of: 8 x + 12 8x+12

4 ( 2 x + 3 ) 4\left(2x+3\right)

2 ( 4 x + 6 ) 2\left(4x+6\right)

2 ( 4 x + 3 ) 2\left(4x+3\right)

4 ( 2 x + 6 ) 4\left(2x+6\right)

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1. Review of Real Numbers1h 27m

Evaluating Exponents
14m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Simplifying Expressions
40m

2. Linear Equations and Inequalities2h 26m

The Addition and Subtraction Properties of Equality
47m

The Multiplication and Division Properties of Equality
30m

Solving Linear Equations
19m

Solving Linear Inequalities
48m

3. Solving Word Problems1h 23m

Introduction to Problem Solving
24m

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21m

Percent Problem Solving
37m

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27m

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11m

Slope of a Line
33m

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25m

Point Slope Form
13m

Introduction to Relations and Functions
25m

Function Notation
15m

5. Systems of Linear Equations1h 25m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
27m

7. Factoring1h 30m

Factoring by Greatest Common Factor & Grouping
26m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Quadratic Equations & Applications
14m

8. Rational Expressions and Equations2h 25m

Simplifying Rational Expressions
29m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
39m

Rational Equations
44m

9. Roots and Radicals1h 21m

Introduction to Radical Expressions
11m

Simplifying Radical Expressions
26m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
23m

10. Quadratic Equations2h 23m

The Square Root Property
17m

Completing the Square
24m

The Quadratic Formula
20m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

Complex Solutions of Quadratic Equations
10m

7. Factoring

Factoring by Greatest Common Factor & Grouping

Beginning Algebra

7. Factoring

Factoring by Greatest Common Factor & Grouping

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Multiple Choice

Factor the GCF out of:
$8 x plus 12$

$2 (4 x + 6)$

$2 (4 x + 3)$

$4 (2 x + 3)$

$4 (2 x + 6)$

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Verified step by step guidance

Identify the terms in the expression: \$8x + 12$.

Find the greatest common factor (GCF) of the coefficients 8 and 12. To do this, list the factors of each number and find the largest one they share.

Once the GCF is found, factor it out of each term in the expression. This means dividing each term by the GCF and writing the expression as the GCF multiplied by the resulting terms inside parentheses.

Write the factored form as $\text{GCF} \times (\text{quotient of first term} + \text{quotient of second term})$.

Double-check by distributing the GCF back through the parentheses to ensure you get the original expression \$8x + 12$.

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