11. Factor the polynomial completely. 2x (3x+6) (x + 2) 6x (x + 2) (x+3) O6x (2x+3)(x+2) 3x (x + 3) (2x + 4) Question 12 12. Perform the indicated operations. **1 623 +30x2+36- +2 ²-16 2²-2x-3 x²+x-12
11. Factor the polynomial completely. 2x (3x+6) (x + 2) 6x (x + 2) (x+3) O6x (2x+3)(x+2) 3x (x + 3) (2x + 4) Question 12 12. Perform the indicated operations. **1 623 +30x2+36- +2 ²-16 2²-2x-3 x²+x-12
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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Question
![### Polynomial Factorization and Rational Expressions
#### Question 11
**Factor the polynomial completely:**
\[ 6x^3 + 30x^2 + 36x \]
Options:
- (A) \( 2x (3x + 6) (x + 2) \)
- (B) \( 6x (x + 2) (x + 3) \)
- (C) \( 6x (2x + 3) (x + 2) \)
- (D) \( 3x (x + 3) (2x + 4) \)
#### Question 12
**Perform the indicated operations.**
\[ \frac{x^2 + x}{x^2 - 16} - \frac{x^2 - 2x - 3}{x^2 + x - 12} \]
Options:
- (A) \( \frac{x}{x - 4} \)
- (B) \( \frac{x}{x - 3} \)
- (C) \( \frac{x}{x - 4} \)
- (D) \( \frac{x}{4} \)
For teachers and students, the above problems involve polynomial factorization and operations with rational expressions, both fundamental concepts in algebra.
In Question 11, you need to factor the polynomial \( 6x^3 + 30x^2 + 36x \) completely by extracting the greatest common factor (GCF) and then factoring further, as necessary.
In Question 12, you are asked to perform subtraction of rational expressions, which requires finding a common denominator, combining the fractions, and simplifying the result.
Understanding these problems and their solutions will enhance your algebraic skills, which are crucial for further mathematical study and practical applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c0554f3-a7d8-4c12-8db7-464a17f00206%2F9c5b1371-bc10-491e-9d4e-d9ab6ce9bfc3%2Fsbmy5ns_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Polynomial Factorization and Rational Expressions
#### Question 11
**Factor the polynomial completely:**
\[ 6x^3 + 30x^2 + 36x \]
Options:
- (A) \( 2x (3x + 6) (x + 2) \)
- (B) \( 6x (x + 2) (x + 3) \)
- (C) \( 6x (2x + 3) (x + 2) \)
- (D) \( 3x (x + 3) (2x + 4) \)
#### Question 12
**Perform the indicated operations.**
\[ \frac{x^2 + x}{x^2 - 16} - \frac{x^2 - 2x - 3}{x^2 + x - 12} \]
Options:
- (A) \( \frac{x}{x - 4} \)
- (B) \( \frac{x}{x - 3} \)
- (C) \( \frac{x}{x - 4} \)
- (D) \( \frac{x}{4} \)
For teachers and students, the above problems involve polynomial factorization and operations with rational expressions, both fundamental concepts in algebra.
In Question 11, you need to factor the polynomial \( 6x^3 + 30x^2 + 36x \) completely by extracting the greatest common factor (GCF) and then factoring further, as necessary.
In Question 12, you are asked to perform subtraction of rational expressions, which requires finding a common denominator, combining the fractions, and simplifying the result.
Understanding these problems and their solutions will enhance your algebraic skills, which are crucial for further mathematical study and practical applications.
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