Chapter 4: Q. 41 (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.
Zeros: $- 1, 1, 3$ ; Degree 3

Short Answer

Expert verified

The polynomial function is $f (x) = x^{3} - 3 x^{3} - x + 3$

Step by step solution

Step 1. Given Information

The zeros of the polynomial are $- 1, 1, 3$ and degree is 3

Step 2. Forming a Polynomial Function

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

means that $x - (- 1), x - 1, x - 3$ are factors of $f .$ . As a result, any polynomial function of the form $f (x) = a (x + 1) (x - 1) (x - 3)$

Step 3. Solving the polynomial function

$f (x) = (x + 1) (x - 1) (x - 3) f (x) = (x^{2} - 1) (x - 3) f (x) = x^{3} - 3 x^{2} - x + 3$

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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: $- 1, 1, 3$ ; Degree 3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Forming a Polynomial Function

Step 3. Solving the polynomial function

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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:-1,1,3; Degree 3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Forming a Polynomial Function

Step 3. Solving the polynomial function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Calculus

Geometry

Pure Maths

Applied Mathematics

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: $- 1, 1, 3$ ; Degree 3