Chapter 4: Q. 44 (page 194)

In Problems 41– 48, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.
$Z e r o s : - 4, 0, 2, d e g r e e 3$

Short Answer

Expert verified

The polynomial function is $f (x) = x^{3} + 2 x^{2} - 8 x$ with degree 3.

Step by step solution

Step 1. Given Information

The zeros of the polynomial are $- 4, 0, 2$ and degree is 3

Step 2. Forming the polynomial function

If $r$ is a real zero of polynomial function, then $x - r$ is factor of $f .$ This means that

$x - (- 4) = x + 4$ and $(x - 0), (x - 2)$ are factors of $f .$ As a result, any polynomial function is of the form $f (x) = a (x + 4) (x - 0) (x - 2) f (x) = x (x + 4) (x - 2)$

Step 3. Solving Polynomial Function

$f (x) = x (x + 4) (x - 2) f (x) = x (x^{2} + 2 x - 8) f (x) = x^{3} + 2 x^{2} - 8 x$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 41– 48, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.
$Z e r o s : - 4, 0, 2, d e g r e e 3$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Forming the polynomial function

Step 3. Solving Polynomial Function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Decision Maths

Geometry

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 41– 48, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.Zeros:-4,0,2,degree3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Forming the polynomial function

Step 3. Solving Polynomial Function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Decision Maths

Geometry

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 41– 48, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.
$Z e r o s : - 4, 0, 2, d e g r e e 3$