**Transcription for Educational Website**---**12. Based on a function whose leading coefficient is -7 and constant is 5, which of the following is a possible rational root?**- a. \( \frac{7}{5} \)- b. \( -\frac{1}{5} \)- c. \( \frac{5}{7} \)- d. \(-7\)---**13. According to the Fundamental Theorem of Algebra (FTA), how many roots does the polynomial \( f(x) = 4x^5 - 3x^2 - x + 5 \) have?**- a. 7- b. 5- c. 8- d. 4---**14. Is \( x = -3 \) a zero of the function \( f(x) = 2x^3 - 5x^2 - 28x + 15 \)?**- a. yes, the remainder is \( r = -60 \)- b. no, the remainder is \( r = 0 \)- c. no, the remainder is \( r = -60 \)- d. yes, the remainder is \( r = 0 \)---

In this question, we can use the rational roots theorem to find the possible rational roots. As per company guidelines, we can only answer one question. So, please repost the other questions and we will definitely help you.12. Rational roots theorem states that if the polynomial has integer coefficients, then the possible rational roots are of the form (pq) where p is the integral factor of the constant term and q is the integral factor of the leading coefficient. So, the possible values of p are 5, -5, 1 and -1. The possible values of q are 7, -7, 1 and -1. Hence the possible rational roots (pq) are 57, -57, 5, -5, 17, -17, 1, -1. So, the correct answer is option C.

Answered: 12. Based on a function whose leading…

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12. Based on a function whose leading coefficient is -7 and constant is 5, which of the following is a possible rational root? a. C. d. –7

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

**Transcription for Educational Website**

---

**12. Based on a function whose leading coefficient is -7 and constant is 5, which of the following is a possible rational root?**

- a. \( \frac{7}{5} \)
- b. \( -\frac{1}{5} \)
- c. \( \frac{5}{7} \)
- d. \(-7\)

---

**13. According to the Fundamental Theorem of Algebra (FTA), how many roots does the polynomial \( f(x) = 4x^5 - 3x^2 - x + 5 \) have?**

- a. 7
- b. 5
- c. 8
- d. 4

---

**14. Is \( x = -3 \) a zero of the function \( f(x) = 2x^3 - 5x^2 - 28x + 15 \)?**

- a. yes, the remainder is \( r = -60 \)
- b. no, the remainder is \( r = 0 \)
- c. no, the remainder is \( r = -60 \)
- d. yes, the remainder is \( r = 0 \)

---

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