Given the polynomial $ y = 10x^3 - 27x^2 + 15x - 2 $,a. List all possible numerators for rational roots of this polynomial: [ ]b. List all possible denominators for rational roots of this polynomial: [ ]c. List all possible rational roots: [ ] **Given the polynomial $ y = 29x - 10x^2 - 21 $:**- **List the possible rational roots:**To find the possible rational roots of a polynomial, you can use the Rational Root Theorem. This theorem states that any rational solution, expressed as $\frac{p}{q}$, will have $p$ as a factor of the constant term and $q$ as a factor of the leading coefficient.For the polynomial $ y = -10x^2 + 29x - 21 $:- The constant term is $-21$.- The leading coefficient is $-10$.**Factors of the constant term ($-21$)**:\[\pm 1, \pm 3, \pm 7, \pm 21\]**Factors of the leading coefficient ($-10$)**:\[\pm 1, \pm 2, \pm 5, \pm 10\]**Possible rational roots** (by the Rational Root Theorem) are combinations of $\frac{p}{q}$:\[\pm 1, \pm \frac{1}{2}, \pm \frac{1}{5}, \pm \frac{1}{10}, \pm 3, \pm \frac{3}{2}, \pm \frac{3}{5}, \pm \frac{3}{10}, \pm 7, \pm \frac{7}{2}, \pm \frac{7}{5}, \pm \frac{7}{10}, \pm 21, \pm \frac{21}{2}, \pm \frac{21}{5}, \pm \frac{21}{10}\]

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Given the polynomial y = 10x³ – 27x? + 15x – 2, a. list all possible numerators for rational roots of this polynomial: b. list all possible denominators for rational roots of this polynomial: c. list all possible rational roots:

Given the polynomial y = 10x³ – 27x? + 15x – 2, a. list all possible numerators for rational roots of this polynomial: b. list all possible denominators for rational roots of this polynomial: c. list all possible rational roots:

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Question

Given the polynomial $ y = 10x^3 - 27x^2 + 15x - 2 $,

a. List all possible numerators for rational roots of this polynomial: [ ]

b. List all possible denominators for rational roots of this polynomial: [ ]

c. List all possible rational roots: [ ]

**Given the polynomial $ y = 29x - 10x^2 - 21 $:**

- **List the possible rational roots:**

To find the possible rational roots of a polynomial, you can use the Rational Root Theorem. This theorem states that any rational solution, expressed as $\frac{p}{q}$, will have $p$ as a factor of the constant term and $q$ as a factor of the leading coefficient.

For the polynomial $ y = -10x^2 + 29x - 21 $:

- The constant term is $-21$.
- The leading coefficient is $-10$.

**Factors of the constant term ($-21$)**:
\[
\pm 1, \pm 3, \pm 7, \pm 21
\]

**Factors of the leading coefficient ($-10$)**:
\[
\pm 1, \pm 2, \pm 5, \pm 10
\]

**Possible rational roots** (by the Rational Root Theorem) are combinations of $\frac{p}{q}$:

\[
\pm 1, \pm \frac{1}{2}, \pm \frac{1}{5}, \pm \frac{1}{10}, \pm 3, \pm \frac{3}{2}, \pm \frac{3}{5}, \pm \frac{3}{10}, \pm 7, \pm \frac{7}{2}, \pm \frac{7}{5}, \pm \frac{7}{10}, \pm 21, \pm \frac{21}{2}, \pm \frac{21}{5}, \pm \frac{21}{10}
\]

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