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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)
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 \( 6x^3 + 17x^2 - 63x + 10 \).
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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