a. Answer The zeroes of polynomial P ( x ) = x 3 + 8 is − 2 , 1 − 3 i , 1 + 3 i Explanation Given information : The polynomial is P ( x ) = x 3 + 8 Calculation : For the zeroes of P ( x ) solve the equation P ( x ) = 0 for x P ( x ) = 0 ⇒ x 3 + 8 = 0 ⇒ x 3 + 2 3 = 0 ( x + 2 ) ( x 2 − 2 x + 2 2 ) = 0 ( x + 2 ) ( x 2 − 2 x + 4 ) = 0 x + 2 = 0 x = − 2 x 2 − 2 x + 4 = 0 x 2 − 2 x = − 4 x 2 − 2 x + 1 = − 4 + 1 ( x − 1 ) 2 = − 3 ( x − 1 ) 2 = − 3 | ( x − 1 ) 2 | = i 3 x − 1 = ± 3 i x = 1 ± 3 i The zeroes of the polynomial function P ( x ) are − 2 , 1 − 3 i , 1 + 3 i b. To determine To calculate : the factored form of polynomial P ( x ) = x 3 + 8 Answer The factored form of polynomial P ( x ) = x 3 + 8 is P ( x ) = ( x + 2 ) , ( x − 1 + 3 i ) , ( x − 1 − 3 i ) Explanation Given information : The polynomial is P ( x ) = x 3 + 8 Calculation : According to the factor theorem if c is a zero of a polynomial function P ( x ) the binomial ( x − c ) is a factor of this polynomial The zeroes of the polynomial is expressed as P ( x ) = ( x + 2 ) , ( x − 1 + 3 i ) , ( x − 1 − 3 i ) Hence, The factored form of polynomial P ( x ) is P ( x ) = ( x + 2 ) ( x − 1 + 3 i ) ( x − 1 − 3 i )

Precalculus: Mathematics for Calculus - 6th Edition

6th Edition

ISBN: 9780840068071

Author: Stewart, James, Redlin, Lothar, Watson, Saleem

Publisher: Cengage Learning

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Question

Chapter 3.6, Problem 13E

To determine

To find: the zeroes of polynomial P(x)=x3+8

Expert Solution

Answer to Problem 13E

The zeroes of polynomial P(x)=x3+8 is −2,1−3i,1+3i

Explanation of Solution

Given information: The polynomial is P(x)=x3+8

Calculation: For the zeroes of P(x) solve the equation P(x)=0 for x

P(x)=0⇒x3+8=0 ⇒x3+23=0(x+2)(x2−2x+22)=0(x+2)(x2−2x+4)=0x+2=0x=−2x2−2x+4=0x2−2x=−4x2−2x+1=−4+1(x−1)2=−3(x−1)2=−3|(x−1)2|=i3x−1=±3ix=1±3i

The zeroes of the polynomial function P(x) are −2,1−3i,1+3i

To determine

To calculate: the factored form of polynomial P(x)=x3+8

Expert Solution

Answer to Problem 13E

The factored form of polynomial P(x)=x3+8 is P(x)=(x+2),(x−1+3i),(x−1−3i)

Explanation of Solution

Given information: The polynomial is P(x)=x3+8

Calculation: According to the factor theorem if c is a zero of a polynomial function P(x) the binomial (x−c) is a factor of this polynomial

The zeroes of the polynomial is expressed as

P(x)=(x+2),(x−1+3i),(x−1−3i)

Hence,

The factored form of polynomial P(x) is

P(x)=(x+2)(x−1+3i)(x−1−3i)

Chapter 3.6, Problem 12E

Chapter 3.6, Problem 14E

Chapter 3 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 3.1 - To put the quadratic function f(x)=ax2+bx+c in...Ch. 3.1 - The quadratic function f(x) = a(x - h)2 + k is in...Ch. 3.1 - The graph of f(x) = 3(x - 2)2 - 6 is a parabola...Ch. 3.1 - The graph of f(x) = -3(x - 2)2 - 6 is a parabola...Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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If c is a real zero of the...Ch. 3.4 - True or False? 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Prob. 80E Ch. 3.7 - Prob. 81E Ch. 3.7 - Prob. 82E Ch. 3.7 - Prob. 83E Ch. 3.7 - Drug Concentration After a certain drug is...Ch. 3.7 - Drug Concentration A drug is administered to a...Ch. 3.7 - Flight of a Rocket Suppose a rocket is fired...Ch. 3.7 - The Doppler Effect As a train moves toward an...Ch. 3.7 - Prob. 88E Ch. 3.7 - Prob. 89E Ch. 3.7 - Prob. 90E Ch. 3.7 - Prob. 91E Ch. 3.7 - Prob. 92E Ch. 3 - Prob. 1RCC Ch. 3 - Prob. 2RCC Ch. 3 - Prob. 3RCC Ch. 3 - Prob. 4RCC Ch. 3 - Prob. 5RCC Ch. 3 - Prob. 6RCC Ch. 3 - Prob. 7RCC Ch. 3 - Prob. 8RCC Ch. 3 - Prob. 9RCC Ch. 3 - Prob. 10RCC Ch. 3 - Prob. 11RCC Ch. 3 - Prob. 12RCC Ch. 3 - Prob. 13RCC Ch. 3 - Prob. 1RE Ch. 3 - Prob. 2RE Ch. 3 - Prob. 3RE Ch. 3 - Prob. 4RE Ch. 3 - Prob. 5RE Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Prob. 8RE Ch. 3 - Prob. 9RE Ch. 3 - Prob. 10RE Ch. 3 - Prob. 11RE Ch. 3 - Prob. 12RE Ch. 3 - Prob. 13RE Ch. 3 - Prob. 14RE Ch. 3 - Prob. 15RE Ch. 3 - Prob. 16RE Ch. 3 - Prob. 17RE Ch. 3 - Prob. 18RE Ch. 3 - Prob. 19RE Ch. 3 - Prob. 20RE Ch. 3 - Prob. 21RE Ch. 3 - Prob. 22RE Ch. 3 - Prob. 23RE Ch. 3 - Prob. 24RE Ch. 3 - Prob. 25RE Ch. 3 - Prob. 26RE Ch. 3 - Prob. 27RE Ch. 3 - Prob. 28RE Ch. 3 - Prob. 29RE Ch. 3 - Prob. 30RE Ch. 3 - Prob. 31RE Ch. 3 - Prob. 32RE Ch. 3 - Prob. 33RE Ch. 3 - Prob. 34RE Ch. 3 - Prob. 35RE Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Prob. 39RE Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Prob. 42RE Ch. 3 - Prob. 43RE Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - Prob. 46RE Ch. 3 - Prob. 47RE Ch. 3 - Prob. 48RE Ch. 3 - Prob. 49RE Ch. 3 - Prob. 50RE Ch. 3 - Prob. 51RE Ch. 3 - Prob. 52RE Ch. 3 - Prob. 53RE Ch. 3 - Prob. 54RE Ch. 3 - Prob. 55RE Ch. 3 - Prob. 56RE Ch. 3 - Prob. 57RE Ch. 3 - Prob. 58RE Ch. 3 - Prob. 59RE Ch. 3 - Prob. 60RE Ch. 3 - Prob. 61RE Ch. 3 - Prob. 62RE Ch. 3 - Prob. 63RE Ch. 3 - Prob. 64RE Ch. 3 - Prob. 65RE Ch. 3 - Prob. 66RE Ch. 3 - Prob. 67RE Ch. 3 - Prob. 68RE Ch. 3 - Prob. 69RE Ch. 3 - Prob. 70RE Ch. 3 - Prob. 71RE Ch. 3 - Prob. 72RE Ch. 3 - Prob. 73RE Ch. 3 - Prob. 74RE Ch. 3 - Prob. 75RE Ch. 3 - Prob. 76RE Ch. 3 - Prob. 77RE Ch. 3 - Prob. 78RE Ch. 3 - Prob. 79RE Ch. 3 - Prob. 80RE Ch. 3 - Prob. 81RE Ch. 3 - Prob. 82RE Ch. 3 - Prob. 83RE Ch. 3 - Prob. 84RE Ch. 3 - Prob. 85RE Ch. 3 - Prob. 86RE Ch. 3 - Express the quadratic function f(x) = x2 x 6 in...Ch. 3 - Find the maximum or minimum value of the quadratic...Ch. 3 - A cannonball fired out to sea from a shore battery...Ch. 3 - Graph the polynomial P(x) = (x + 2)3 + 27, showing...Ch. 3 - (a) Use synthetic division to find the quotient...Ch. 3 - Let P(x) = 2x3 5x2 4x + 3. (a) List all possible...Ch. 3 - Prob. 7T Ch. 3 - Find all real and complex zeros of P(x) = x3 x2 ...Ch. 3 - Find the complete factorization of P(x) = x4 2x3...Ch. 3 - Find a fourth-degree polynomial with integer...Ch. 3 - Let P(x) = 2x4 7x3 + x2 18x + 3. (a) Use...Ch. 3 - Prob. 12T Ch. 3 - Prob. 1P Ch. 3 - Prob. 2P Ch. 3 - How Fast Can You List Your Favorite Things? If you...Ch. 3 - Prob. 4P Ch. 3 - Height of a Baseball A baseball is thrown upward,...Ch. 3 - Torricelli's Law Water in a tank will flow out of...

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the zeroes of polynomial P ( x ) = x 3 + 8

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To find: the zeroes of polynomial P(x)=x3+8

Answer to Problem 13E

Explanation of Solution

To calculate: the factored form of polynomial P(x)=x3+8

Answer to Problem 13E

Explanation of Solution

Chapter 3 Solutions