Factor by grouping (sometimes called the ac-method). 5x² +12x+4 First, choose a form with appropriate signs. Then, fill in the blanks with numbers to be used for grouping. Finally, show the factorization. Form: X S ? 0x + 0x + 4 1- -4 x-4 x + 4 O O X₁ X + + I U RN I U X X Factorization: m Explanation CEIS110_Project_....pptx - 30 - X Check
Factor by grouping (sometimes called the ac-method). 5x² +12x+4 First, choose a form with appropriate signs. Then, fill in the blanks with numbers to be used for grouping. Finally, show the factorization. Form: X S ? 0x + 0x + 4 1- -4 x-4 x + 4 O O X₁ X + + I U RN I U X X Factorization: m Explanation CEIS110_Project_....pptx - 30 - X Check
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![# Factoring a Quadratic by the AC-Method
## Exponents and Polynomials
### Factoring by Grouping (Sometimes Called the AC-Method)
#### Example:
\[ 5x^2 + 12x + 4 \]
First, choose a form with appropriate signs. Then, fill in the blanks with numbers to be used for grouping. Finally, show the factorization.
#### Form:
There are three possible forms to choose from:
1. \( 5x^2 + \_x + \_x + 4 \)
- There are two blank boxes in the equation where you will need to fill in the appropriate coefficients for the middle-term splitting.
2. \( 5x^2 + \_x - \_x + 4 \)
- This form includes a negative sign in the third term, indicating we may need negative coefficients to correctly factor the quadratic expression.
3. \( 5x^2 - \_x + \_x + 4 \)
- Similarly, this form features a negative sign in the second term for appropriate splitting.
#### Factorization:
After choosing one of the forms and filling in the blanks with the appropriate values, the factored form of the quadratic expression is displayed.
#### Actions:
- **Explanation**: Provides a detailed explanation of the factoring process.
- **Check**: Allows verification of your factorization.
#### Example Calculation:
To factor \( 5x^2 + 12x + 4 \), follow these steps:
1. Identify the coefficients \(a = 5\), \(b = 12\), and \(c = 4\).
2. Multiply \(a\) and \(c\):
\[ 5 \cdot 4 = 20 \]
3. Find two numbers that multiply to 20 and add up to \( b\):
- The numbers are 10 and 2 because \(10 \times 2 = 20\) and \(10 + 2 = 12\).
4. Use these numbers to rewrite and factor the quadratic:
\[ 5x^2 + 10x + 2x + 4 \]
5. Group the terms:
\[ (5x^2 + 10x) + (2x + 4) \]
6. Factor out the greatest common factor from each group:
\[ 5x(x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8175d67d-08a3-43eb-bfb3-8ec86236d575%2F037086bb-0815-461e-a8f8-4b191cc3f328%2Fjooxwoh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Factoring a Quadratic by the AC-Method
## Exponents and Polynomials
### Factoring by Grouping (Sometimes Called the AC-Method)
#### Example:
\[ 5x^2 + 12x + 4 \]
First, choose a form with appropriate signs. Then, fill in the blanks with numbers to be used for grouping. Finally, show the factorization.
#### Form:
There are three possible forms to choose from:
1. \( 5x^2 + \_x + \_x + 4 \)
- There are two blank boxes in the equation where you will need to fill in the appropriate coefficients for the middle-term splitting.
2. \( 5x^2 + \_x - \_x + 4 \)
- This form includes a negative sign in the third term, indicating we may need negative coefficients to correctly factor the quadratic expression.
3. \( 5x^2 - \_x + \_x + 4 \)
- Similarly, this form features a negative sign in the second term for appropriate splitting.
#### Factorization:
After choosing one of the forms and filling in the blanks with the appropriate values, the factored form of the quadratic expression is displayed.
#### Actions:
- **Explanation**: Provides a detailed explanation of the factoring process.
- **Check**: Allows verification of your factorization.
#### Example Calculation:
To factor \( 5x^2 + 12x + 4 \), follow these steps:
1. Identify the coefficients \(a = 5\), \(b = 12\), and \(c = 4\).
2. Multiply \(a\) and \(c\):
\[ 5 \cdot 4 = 20 \]
3. Find two numbers that multiply to 20 and add up to \( b\):
- The numbers are 10 and 2 because \(10 \times 2 = 20\) and \(10 + 2 = 12\).
4. Use these numbers to rewrite and factor the quadratic:
\[ 5x^2 + 10x + 2x + 4 \]
5. Group the terms:
\[ (5x^2 + 10x) + (2x + 4) \]
6. Factor out the greatest common factor from each group:
\[ 5x(x
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