Answer :

carlosego
You have the following expression given in the problem:

f(x) = x³ – 2x² – x + 2

 Therefore, to find the roots, you must apply the proccedure shown below:

 1. You have:

 0 = x3 – 2x2 – x + 2

 2. Then, when you factor, you obtain:

 (x-2)(x-1)(x+1)=0

 3. Therefore, you have that the roots are the following:

 x1=-1
 x2=1
 x3=2
abidemiokin

The zeros of the given polynomial function are 1, -1 and 2

Given the polynomial function [tex]f(x) = x^3 - 2x^2 - x + 2,[/tex]

First, we need to assume a value of x to check if it will give us zero after substituting:

Assuming x = 1

[tex]f(1) = 1^3 - 2(1)^2 - 1 + 2\\f(1) = 1 - 2 - 1 + 2\\f(1) = 0[/tex]

Since f(1) =0, hence x - 1 is a factor

Dividing x - 1 by the given polynomial function, we will have:

[tex]\frac{x^3-2x^2-x+2}{x-1} \\= \frac{x^2(x-2)-1(x-2)}{x-1} \\=\frac{(x^2-1)(x-2)}{x-1}\\=\frac{(x+1)(x-1)(x-2)}{x-1}\\=(x+1)(x-2)[/tex]

Equating the result to zero

x + 1 = 0 and x - 2 = 0

x = -1 and 2

Hence the zeros of the given polynomial function are 1, -1 and 2

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