4. Factor f(x) into linear factors given that k is a zero. f(x) = 6x3 + 17x² – 63x +10;k=-5 a. f(x) = (x+ 5)(6x - 1)(x- 2) b. f(x) = (x + 5)(6x + 1)(x+ 2) %3D d. f(x) = (x + 5)(6x – 1)(x+ 2)
4. Factor f(x) into linear factors given that k is a zero. f(x) = 6x3 + 17x² – 63x +10;k=-5 a. f(x) = (x+ 5)(6x - 1)(x- 2) b. f(x) = (x + 5)(6x + 1)(x+ 2) %3D d. f(x) = (x + 5)(6x – 1)(x+ 2)
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 Polynomial Expressions
---
#### Problem Statement
Factor \( f(x) \) into linear factors given that \( k \) is a zero. The polynomial \( f(x) \) is given by:
\[ f(x) = 6x^3 + 17x^2 - 63x + 10 \]
where \( k = -5 \).
#### Options to Consider:
a. \( f(x) = (x + 5)(6x - 1)(x - 2) \)
b. \( f(x) = (x + 5)(6x + 1)(x + 2) \)
c. \( f(x) = (x + 5)(6x + 1)(x - 2) \)
d. \( f(x) = (x + 5)(6x - 1)(x + 2) \)
### Steps to Factor the Polynomial
1. Given that \( k = -5 \) is a zero of \( f(x) \), we know that \( (x + 5) \) is a factor.
2. We must determine the other factors that will multiply with \( (x + 5) \) to give the original polynomial.
3. Consider each option and verify by performing polynomial multiplication to ensure the terms match \( 6x^3 + 17x^2 - 63x + 10 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46d3de30-8cd0-41b8-93a1-561135287d7d%2F9393b4ce-0c3a-43a2-ab48-2f23d48bc063%2Falwg3du_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Factoring Polynomial Expressions
---
#### Problem Statement
Factor \( f(x) \) into linear factors given that \( k \) is a zero. The polynomial \( f(x) \) is given by:
\[ f(x) = 6x^3 + 17x^2 - 63x + 10 \]
where \( k = -5 \).
#### Options to Consider:
a. \( f(x) = (x + 5)(6x - 1)(x - 2) \)
b. \( f(x) = (x + 5)(6x + 1)(x + 2) \)
c. \( f(x) = (x + 5)(6x + 1)(x - 2) \)
d. \( f(x) = (x + 5)(6x - 1)(x + 2) \)
### Steps to Factor the Polynomial
1. Given that \( k = -5 \) is a zero of \( f(x) \), we know that \( (x + 5) \) is a factor.
2. We must determine the other factors that will multiply with \( (x + 5) \) to give the original polynomial.
3. Consider each option and verify by performing polynomial multiplication to ensure the terms match \( 6x^3 + 17x^2 - 63x + 10 \).
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