Calculus: An Applied Approach (MindTap Course List)
10th Edition
ISBN: 9781305860919
Author: Ron Larson
Publisher: Cengage Learning
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Chapter A4, Problem 66E
To determine
To calculate: The all real zeros of the polynomial
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Describe how to use Descartes’s Rule of Signs to determine the possible number of positive real zeros of a polynomial function.
Part A: Create a fourth degree polynomial with three terms in standard form. How do you know it is in standard form?
Part B : Explain the closure property as it relates to addition of polynomials. Give an example.
MAT109
Test 2
Given (-3 + i) is a root of the polynomial f(x) = 4x3 + 23x² + 34x – 10, find all roots
and write the function in factored form with linear terms of the form (ax - b).
a) Irrational roots:
b) Rational roots:
c) Factored form:
Chapter A4 Solutions
Calculus: An Applied Approach (MindTap Course List)
Ch. A4 - Prob. 1CPCh. A4 - Prob. 2CPCh. A4 - Prob. 3CPCh. A4 - Prob. 4CPCh. A4 - Prob. 1ECh. A4 - Prob. 2ECh. A4 - Prob. 3ECh. A4 - Prob. 4ECh. A4 - Prob. 5ECh. A4 - Prob. 6E
Ch. A4 - Prob. 7ECh. A4 - Prob. 8ECh. A4 - Prob. 9ECh. A4 - Prob. 10ECh. A4 - Prob. 11ECh. A4 - Prob. 12ECh. A4 - Prob. 13ECh. A4 - Prob. 14ECh. A4 - Prob. 15ECh. A4 - Prob. 16ECh. A4 - Factoring Polynomials In Exercises 9-18, write the...Ch. A4 - Prob. 18ECh. A4 - Prob. 19ECh. A4 - Prob. 20ECh. A4 - Prob. 21ECh. A4 - Prob. 22ECh. A4 - Prob. 23ECh. A4 - Prob. 24ECh. A4 - Prob. 25ECh. A4 - Prob. 26ECh. A4 - Prob. 27ECh. A4 - Prob. 28ECh. A4 - Prob. 29ECh. A4 - Prob. 30ECh. A4 - Prob. 31ECh. A4 - Prob. 32ECh. A4 - Prob. 33ECh. A4 - Prob. 34ECh. A4 - Prob. 35ECh. A4 - Prob. 36ECh. A4 - Prob. 37ECh. A4 - Prob. 38ECh. A4 - Prob. 39ECh. A4 - Prob. 40ECh. A4 - Prob. 41ECh. A4 - Prob. 42ECh. A4 - Prob. 43ECh. A4 - Prob. 44ECh. A4 - Prob. 45ECh. A4 - Prob. 46ECh. A4 - Prob. 47ECh. A4 - Prob. 48ECh. A4 - Prob. 49ECh. A4 - Prob. 50ECh. A4 - Prob. 51ECh. A4 - Prob. 52ECh. A4 - Prob. 53ECh. A4 - Prob. 54ECh. A4 - Prob. 55ECh. A4 - Prob. 56ECh. A4 - Prob. 57ECh. A4 - Prob. 58ECh. A4 - Prob. 59ECh. A4 - Prob. 60ECh. A4 - Prob. 61ECh. A4 - Prob. 62ECh. A4 - Prob. 63ECh. A4 - Prob. 64ECh. A4 - Prob. 65ECh. A4 - Prob. 66ECh. A4 - Prob. 67ECh. A4 - Prob. 68ECh. A4 - Prob. 69ECh. A4 - Prob. 70ECh. A4 - Prob. 71ECh. A4 - Prob. 72ECh. A4 - Prob. 73ECh. A4 - Prob. 74ECh. A4 - Prob. 75ECh. A4 - Prob. 76E
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- In Exercises 2-6, fill in the blanks. The Theorem states that if a polynomial f(x)is divided by xk,then the remainder is r=f(k).arrow_forwardIn Exercises 2-6, fill in the blanks. The Theorem states that a polynomial f(x)has a factor (xk)if and only if f(k)=0.arrow_forwardUse synthetic division to show that x=3 is a zero of the function f(x)=2x35x26x+15. Use the result to factor the polynomial function completely and list all the zeros of the function.arrow_forward
- Approximating Zeros In Exercises 71-76, (a) use the zero or root feature of a graphing utility to approximate the zeros of the function accurate to three decimal places, (b) determine the exact value of one of the zeros, and (c) use synthetic division to verify your result from part (b), and then factor the polynomial completely. h(t)=t32t27t+2arrow_forwardUse the Rational Zero Theorem to help you find the zeros of the polynomial functions. f(x)=2x3+5x26x9arrow_forwardIn Exercises 33-48, (a) find all real zeros of the polynomial function, (b) determine whether the multiplicity of each zero is even or odd, (c) determine the maximum possible number of turning points of the graph of the function, and (d) use a graphing utility to graph the function and verify your answers. f(x)=x4x330x2arrow_forward
- Explain why the Rational Zero Theorem does notguarantee finding zeros of a polynomial function.arrow_forwardTrue or False? In Exercises 83-86, determine whether the statement is true or false. Justify your answer. If (7x+4)is a factor of some polynomial function f(x), then 47is a zero of f.arrow_forwardFill in the blanks. When a real zero xa of a polynomial functionfis of even multiplicity, the graph of fthe x-axisatx=a,and when it is of odd multiplicity, the graph of f the x-axisatx=a.arrow_forward
- Error Analysis Describe the error in finding a polynomial function f with real coefficients that has 2,3.5, and i as zeros. A function is fx=x+2x3.5xi.arrow_forwardUse the Rational Zero Theorem to list all possible rational zeros of the polynomial function. P(x)=x3+10x2+5x12arrow_forwardFinding Real Zeros of a Polynomial Function In Exercises 33-48, (a) find all real zeros of the polynomial function, (b) determine whether the multiplicity of each zero is even or odd, (c) determine the maximum possible number of turning points of the graph of the function, and (d) use a graphing utility to graph the function and verify your answers. f(x)=81x2arrow_forward
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