Answered: y = 2r3 + x² – 13x + 6 [-4, 0, 1] by…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 28E

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Question

Use the graph or the table to determine a solution of the given equation 2x³ + x² - 13x + 6 = 0. Use synthetic division to verify that this number is a solution of the equation. Then solve the polynomial equation.

y = 2r3 + x² – 13x + 6
[-4, 0, 1] by [-25, 25, 5]

Expert Solution

Step 1

Given Data

The equation is $y = 2 x^{3} + x^{2} - 13 x + 6$ .

The x-intercept is -3 as shown in the graph. So the solution is -3.

By using the factor theorem f(-3)=0 then x+3 is factor of the equation.

Divide the equation $y = 2 x^{3} + x^{2} - 13 x + 6$ by x+3 by using the synthetic division,

$- 3 2 1 - 13 6 - 6 15 - 6 2 - 5 2 0$

The remainder is 0.

Hence the solution is correct.

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