Factor completely.2x2+9x+92x^2+9x+9

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

Factor completely. 2 x 2 + 9 x + 9 2x^2+9x+9

For this problem, we've been asked to factor this trinomial completely, and we're going to use the method that we've been learning recently, called the AC method, or also known as the grouping method. So our first step is to identify our a value, our c value, as well as our b value. And next, we want to multiply our a and c value and find all of its factor pairs. So our a value is two, and our c value is nine. So multiplying those together, we get 18. And we wanna identify a pair of factors that multiply to 18 and also add to our b value of nine. So what are some factors of 18? Well, we have two and nine, which combine to make 11. We also have three and six, which combine to make nine. So that tells me that this is the factor pair that I am looking for. So now that we've identified our factor pair, we're going to split apart our middle term to turn this three term polynomial into a four term polynomial. So we can rewrite our polynomial as a two x squared, plus three x, plus six x, plus nine. And now we're going to apply factoring by grouping. So let's start by grouping our first two terms and last two terms and seeing if that works out. For our first two terms, our GCF is x, and for our last two terms, our GCF is three. So since both set of terms have a GCF, we can now continue our factoring by grouping by factoring them out. Factoring out x, we're left with two x plus three, and factoring out three, we are also left with two x plus three, which is perfect because now we have a common binomial that we can also factor out. So factoring out two x plus three, we're left with x plus three, and this here is our final answer.

Factor $$completely.2x2+9x+92x^2+9x+9$$

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

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

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

(x−3)(2x−3)\left(x-3\right)\left(2x-3\right)

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1. Review of Real Numbers2h 24m

Simplifying Fractions
30m

Evaluating Exponents
14m

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 42m

The Addition and Subtraction Properties of Equality
47m

The Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Solving Linear Inequalities
1h 8m

3. Solving Word Problems2h 48m

Introduction to Problem Solving
37m

Formulas
21m

Percent Problem Solving
1h 4m

Mixture Problem Solving
43m

4. Graphing4h 42m

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

Linear Inequalities in Two Variables
28m

Introduction to Relations and Functions
40m

Function Notation
15m

5. Systems of Linear Equations2h 6m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

Systems of Linear Inequalities
23m

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 36m

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
35m

8. Rational Expressions and Equations3h 51m

Simplifying Rational Expressions
39m

Multiplying and Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
24m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
39m

Rational Equations
44m

Direct & Inverse Variation
27m

9. Roots and Radicals2h 46m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
46m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

10. Quadratic Equations3h 2m

The Square Root Property
17m

Completing the Square
24m

The Quadratic Formula
29m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

Complex Solutions of Quadratic Equations
10m

Graphing Quadratic Equations
30m

7. Factoring

Factoring Trinomials of the Form ax² + bx + c

Beginning Algebra

7. Factoring

Factoring Trinomials of the Form ax² + bx + c

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Multiple Choice

Factor completely.
$2 x^{2} + 9 x + 9$

$(2 x + 3) (x + 3)$

$(2 x + 3) (x - 3)$

$(x + 3) (2 x - 3)$

$(x - 3) (2 x - 3)$

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Verified step by step guidance

Identify the quadratic expression to factor: $2x^{2} + 9x + 9$.

Multiply the coefficient of $x^{2}$ (which is 2) by the constant term (which is 9) to get $2 \times 9 = 18$.

Find two numbers that multiply to 18 and add up to the middle coefficient, 9. These numbers are 6 and 3 because $6 \times 3 = 18$ and $6 + 3 = 9$.

Rewrite the middle term \$9x$ as $6x + 3x$, so the expression becomes $2x^{2} + 6x + 3x + 9$.

Group the terms in pairs and factor each group: from the first two terms, factor out \$2x$ to get \(2x(x + 3)$; from the last two terms, factor out 3 to get $3(x + 3)$. Then factor out the common binomial \)(x + 3)$ to get $(2x + 3)(x + 3)$.

8:18m

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