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Consider the polynomial equation 4 - 2x²16-150 a) Use synthetic division to show that x=3 is a solution to the polynomial equation but x=-3 is NOT a solution. b) Explain, without any detailed calculation that x=2 cannot be a solution to the polynomial. c) Factor the polynomial completely.

Consider the polynomial equation 4 - 2x²16-150 a) Use synthetic division to show that x=3 is a solution to the polynomial equation but x=-3 is NOT a solution. b) Explain, without any detailed calculation that x=2 cannot be a solution to the polynomial. c) Factor the polynomial completely.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.2: Properties Of Division
Problem 26E
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Question
Consider the polynomial equation \(x^4 - 2x^2 - 16x - 15 = 0\) a) Use synthetic division to show that \( x = 3 \) is a solution to the polynomial equation but \( x = -3 \) is NOT a solution. b) Explain, without any detailed calculation that \( x = 2 \) cannot be a solution to the polynomial. c) Factor the polynomial completely.
Transcribed Image Text:Consider the polynomial equation \(x^4 - 2x^2 - 16x - 15 = 0\) a) Use synthetic division to show that \( x = 3 \) is a solution to the polynomial equation but \( x = -3 \) is NOT a solution. b) Explain, without any detailed calculation that \( x = 2 \) cannot be a solution to the polynomial. c) Factor the polynomial completely.
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