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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 4: Q. 45 (page 194)

In Problems 41鈥� 48, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.
$Z e r o s : - 4, - 1, 2, 3; d e g r e e 4$

Short Answer

Expert verified

The polynomial function is $f (x) = x^{4} - 15 x^{2} + 10 x + 24$ with degree 4.

Step by step solution

01

Step 1. Given Information

The zeros of the polynomial are $- 4, - 1, 2, 3$ and degree is 4.

02

Step 2. Forming the polynomial Function

If $r$ a real zero of a polynomial function of $f,$ then $x - r$ is a factor of $f .$ This means that $x - (- 4) = x + 4$ and $(x + 1), (x - 2), (x - 3)$ are the factors of $f .$ Any polynomial function is of the form $f (x) = a (x + 4) (x + 1) (x - 2) (x - 3) i f a = 1 f (x) = (x + 4) (x + 1) (x - 2) (x - 3)$

03

Step 3. Solving Polynomial Function

$f (x) = (x + 4) (x + 1) (x - 2) (x - 3) f (x) = (x^{2} + 5 x + 4) (x^{2} - 5 x + 6) f (x) = (x^{4} - 5 x^{3} + 6 x^{2} + 5 x^{3} - 25 x^{2} + 30 x + 4 x^{2} - 20 x + 24) f (x) = x^{4} - 15 x^{2} + 10 x + 24$

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Most popular questions from this chapter

Write a few paragraphs that provide a general strategy for graphing a polynomial function. Be sure to mention the following: degree, intercepts, end behavior, and turning points.

Find the domain of the rational function.

$G (x) = \frac{6}{(x + 3) (4 - x)}$

Factor the expression $6 x^{2} + x - 2$ .

True or False : A test number for the interval $- 2 < x < 5$ could be 4.

Find the domain of the rational function.

$R (x) = \frac{4 x}{x - 3}$

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