High School

We appreciate your visit to The incomplete graph to the right shows the following polynomial function tex f x 3x 5 2x 4 60x 3 40x 2 192x 128 tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

The incomplete graph to the right shows the following polynomial function:

[tex] f(x) = -3x^5 - 2x^4 + 60x^3 + 40x^2 - 192x - 128 [/tex]

a. What are the zeros of the function?

The zeros are: [tex]\square[/tex]

(Simplify your answer. Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

Answer :

To find the zeros of the polynomial function [tex]\( f(x) = -3x^5 - 2x^4 + 60x^3 + 40x^2 - 192x - 128 \)[/tex], we need to determine the values of [tex]\( x \)[/tex] that make the function equal to zero. These values are the solutions to the equation:

[tex]\[ f(x) = 0 \][/tex]

For polynomials, finding the zeros can sometimes involve factoring the polynomial or using techniques like the Rational Root Theorem, synthetic division, or other algebraic methods.

The zeros of the given polynomial function are:

- [tex]\( x = -4 \)[/tex]
- [tex]\( x = -2 \)[/tex]
- [tex]\( x = -\frac{2}{3} \)[/tex]
- [tex]\( x = 2 \)[/tex]
- [tex]\( x = 4 \)[/tex]

This means if you substitute any of these values into the polynomial for [tex]\( x \)[/tex], you'll get [tex]\( f(x) = 0 \)[/tex]. These solutions represent the points where the graph of the function crosses the x-axis.

If you have further questions about polynomial zeros or need help with related concepts, feel free to ask!

Thanks for taking the time to read The incomplete graph to the right shows the following polynomial function tex f x 3x 5 2x 4 60x 3 40x 2 192x 128 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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