/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 8 Use the Rational Zero Theorem to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 8

Use the Rational Zero Theorem to list possible rational zeros for each polynomial function. $$P(x)=x^{3}-19 x-30$$

Short Answer

Expert verified
The possible rational zeros of the function are \(\pm 1, \pm 2, \pm 3, \pm 5, \pm 6, \pm 10, \pm 15, \pm 30\).

Step by step solution

01

Listing Factors

List all pairs of factors of the constant term -30. These factors are \(\pm 1, \pm 2, \pm 3, \pm 5, \pm 6, \pm 10, \pm 15, \pm 30\). Each factor is listed with its positive and negative counterpart because the factor could lead to a positive or negative zero.
02

Write out Factors of Leading Coefficient

Next, list all factors of the leading coefficient 1. In this case, the only factors are \(\pm 1\).
03

Apply the Rational Zero Theorem

Finally, apply the Rational Zero Theorem by writing the ratio of each factor of the constant term to each factor of the leading coefficient. In this case, the lone factor of the leading coefficient is 1, so each ratio is just each factor of -30. So, the list of possible rational zeros of the function is \(\pm 1, \pm 2, \pm 3, \pm 5, \pm 6, \pm 10, \pm 15, \pm 30\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find a polynomial function of lowest degree with integer coefficients that has the given zeros. $$4,-3,2$$

Find the zeros of each polynomial function. If a zero is a multiple zero, state its multiplicity. $$P(x)=x^{3}-8 x^{2}+8 x+24$$

In Exercises 61 to 70 , use the quadratic formula to solve each quadratic equation. $$x^{2}-4 x=1$$

Find the zeros of each polynomial function. If a zero is a multiple zero, state its multiplicity. $$P(x)=x^{3}-7 x^{2}-7 x+69$$

Find the zeros of each polynomial function. If a zero is a multiple zero, state its multiplicity. $$P(x)=x^{4}+x^{3}-3 x^{2}-5 x-2$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.