### Finding the Zeros of a Polynomial FunctionIn this exercise, you are required to find all the zeros of the polynomial function given below:\[ f(x) = 4x^3 + 32x^2 - 72x + 60 \]**Instructions:**1. Determine the exact values of all the zeros of the polynomial.2. Enter the zeros separated by commas.3. Provide exact values rather than decimal approximations.**Input Field:**Below the problem statement, there is a text box where you should enter the zeros separated by commas.For example, if the zeros were \( x = -3 \), \( x = 1 \), and \( x = 5 \), you would enter the following in the text box:\[ -3, 1, 5 \]**Note:**This problem is designed to test your ability to factorize polynomials and solve for their roots. **Example:** To solve \( f(x) = 0 \):1. Apply polynomial division if necessary.2. Use synthetic division to test potential rational roots.3. Factorize the polynomial completely.Keep in mind to verify your solutions by substituting them back into the polynomial to confirm that they indeed produce zero.Happy solving!

Answered: Image /qna-images/answer/2b7d2adc-0d69-4824-9ab4-7647b5719d86.jpg

Answered: Find all zeros of f(x) = 4x³ + 32x² +…

Find all zeros of f(x) = 4x³ + 32x² + 72x + 60. Enter the zeros separated by commas. Enter exact value, not decimal approximations.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: Find the real zeros of the polynomial function. f(x) = 4x³ - 5x² − 7x + 2 O-1, 2, 4 01, -2, -4 01,…

Q: Write a polynomial that has the zeros at 3,-8,-5/2, and -1.

A: Since 3,-8,-5/2,-1 are zeros. (x-3),(x+8),(x+5/2),(x+1) has its factors Therefore,…

Q: Create a cubic expression that when divided by (x-1) will have a remainder of 6

Q: State the Factor Theorem. What is its relationship to the zeros of a polynomial function

A: We have to state factor theorem.

Q: Find the remaining zeros of each function and write in factored form. 13. f(x) = x + 3x³ - 29x² - 3x…

Q: Find all the real zeros of the polynomial. Use the quadratic formula if necessary. 1.…

Q: 5x+21x° -LX+Xナ4X+L

Q: Let f(x) = 2(x - 1)² - 10.

A: The given polynomial .The objective is to write the polynomial into factored form.

Q: writes (x+ 5r + 2r - 8) = (x – 1)(?x²+?x+?) and draws a diagram. Priya wants to sketch a graph of…

A: We have to factorise the polynomial function. And draw the graph.

Q: Write a polynomial with degree 3 that has zeros at x=−5/2 and x=2+√5. Write the function using only…

Q: please create two polynomials with different degrees but the same characteristics: crosses the…

Q: Given that the polynomial has the given zero, find the other zeros. f(x) =x3-8;2 please write down…

A: Given query is to find the zeros of the function.

Q: Find all the zeros of the following polynomial function

Q: Need it asap. Thank youu! The polynomial function : M(x) = 15x ^ 6 - 2x ^ 3 - 4x ^ 2 + 6x + 8 can…

A: From the given function: Mx=15x6-2x3-4x2+6x+8 So, a). At x=1 hour.…

Question

### Finding the Zeros of a Polynomial Function

In this exercise, you are required to find all the zeros of the polynomial function given below:

\[ f(x) = 4x^3 + 32x^2 - 72x + 60 \]

**Instructions:**
1. Determine the exact values of all the zeros of the polynomial.
2. Enter the zeros separated by commas.
3. Provide exact values rather than decimal approximations.

**Input Field:**
Below the problem statement, there is a text box where you should enter the zeros separated by commas.

For example, if the zeros were \( x = -3 \), \( x = 1 \), and \( x = 5 \), you would enter the following in the text box:
\[ -3, 1, 5 \]

**Note:**
This problem is designed to test your ability to factorize polynomials and solve for their roots.

**Example:** To solve \( f(x) = 0 \):
1. Apply polynomial division if necessary.
2. Use synthetic division to test potential rational roots.
3. Factorize the polynomial completely.

Keep in mind to verify your solutions by substituting them back into the polynomial to confirm that they indeed produce zero.

Happy solving!

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Hit and Trial Method

VIEW

Step 2: Explanation

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Use the written statement to construct a polynomial function that represents the required information.A rectangle is twice as long as it is wide. Squares with sides measuring 3 feet are cut out from each corner. Then the sides are folded up to make an open box. Express the volume V of the box as a function of the width x, where V is measured in square feet. V(x) =
write the quadratic polynomial in shifted form (i.e., complete the square) a. f(x)= x^2+6x+1 b. f(x)= -3x^2+24x-8
write a polynomial function for each set of zeros. x=-3,2,4 A. X^3 -3x^2-12x+4 B. X^3-3x^2-10x+12 C. X^3-3x^2-10x+24 D. X^3-4x^2+8x-8
Write a polynomial function f of the least degree that has rational coefficients, a leading coefficient of 1, and the zeros 4 and square root (6). Only type the coefficients of your answer in the blanks for the standard form: Ax^3+Bx^2+Cx+D Type negative numbers when the term is subtracted and type 0 when the term is missing.
The measurements of the rectangle below is shown in the diagram. Express the area of the rectangle as a polynomial in terms of H.
Write a polynomial function f (x) in expanded form where the only zeros are −4, 3 and 6.