Factor the GCF out of:6x2+9x6x^2+9x

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

Factor the GCF out of: 6 x 2 + 9 x 6x^2+9x

Here, we're asked to factor the polynomial six x squared plus nine x by factoring out the greatest common factor. So first, let's identify what the greatest common factor is. To do that, we're going to write out the prime factorization for each of our terms. The prime factors for six x squared are two times three times x times x, and the prime factors for nine x are three times three times x. So the factors that they have in common are three and x, which means our greatest common factor is three times x. So now I'm going to rewrite each of the terms in our polynomial as a product with the greatest common factor. So what can I multiply three x by to get six x squared? Well that would be two x, so I can rewrite it as three x times two x. And what can I multiply three x by to get nine x? Well, that would be three. So I can rewrite nine x as three x times three. Now I'm going to factor out three x, and I'm left with two x plus three. So this here is our final answer.

Factor the GCF out of: 6 x 2 + 9 x 6x^2+9x

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

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

6 x ( x + 3 ) 6x\left(x+3\right)

3 x ( 2 x + 6 ) 3x\left(2x+6\right)

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1. Review of Real Numbers2h 39m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
40m

2. Linear Equations and Inequalities3h 38m

The Addition and Subtraction Properties of Equality
41m

The Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Linear Inequalities in One Variable
1h 11m

3. Solving Word Problems2h 43m

Introduction to Problem Solving
37m

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21m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphing Linear Equations in Two Variables3h 17m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

5. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

6. Exponents and Polynomials3h 25m

The Product Rule
10m

The Quotient Rule
13m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

7. Factoring2h 42m

Factoring by Greatest Common Factor & Grouping
37m

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

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

Factoring Special Products
33m

Quadratic Equations & Applications
41m

8. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

Multiplying and Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

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44m

9. Inequalities and Absolute Value2h 52m

Set Operations and Compound Inequalities
42m

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38m

Absolute Value Inequalities
39m

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28m

Systems of Linear Inequalities
23m

10. Relations and Functions1h 10m

Introduction to Relations and Functions
25m

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15m

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5m

Composition of Functions
24m

11. Roots, Radicals, and Complex Numbers2h 33m

Introduction to Radical Expressions
11m

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27m

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19m

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23m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

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25m

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26m

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31m

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Introduction to Inverse Functions
25m

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13m

Introduction to Logarithmic Functions
26m

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32m

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15m

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10m

15. Sequences, Series, and the Binomial Theorem1h 20m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Factorials
11m

7. Factoring

Factoring by Greatest Common Factor & Grouping

Beginning & Intermediate Algebra

7. Factoring

Factoring by Greatest Common Factor & Grouping

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Multiple Choice

Factor the GCF out of:
$6 x squared plus 9 x$

$3 x (2 x + 3)$

$3 (2 x^{2} + 3 x)$

$6 x (x + 3)$

$3 x (2 x + 6)$

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Verified step by step guidance

Identify the terms in the expression: \$6x^2 + 9x$.

Find the greatest common factor (GCF) of the coefficients 6 and 9. The GCF is the largest number that divides both 6 and 9 evenly.

Determine the common variable factors in each term. Both terms have at least one $x$, so include $x$ in the GCF.

Write the GCF by combining the numerical GCF and the common variable factor(s).

Factor out the GCF from each term by dividing each term by the GCF and write the expression as the product of the GCF and the resulting binomial.

5:42m

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