Respuesta :
Answer:
B. −2
C. −1
E. 1
Step-by-step explanation:
He have been given a polynomial function [tex]f(x)=x^3+2x^2-x-2[/tex]. We are asked to find the zeros of our given function.
To find the zeros of our given function, we will equate our function with zero and solve for x as:
[tex]x^3+2x^2-x-2=0[/tex]
Now, we will factor our equation by grouping method.
[tex](x^3+2x^2)-(x+2)=0[/tex]
[tex]x^2(x+2)-1(x+2)=0[/tex]
[tex](x+2)(x^2-1)=0[/tex]
Now, we will use difference of squares [tex]a^b-b^2=(a+b)(a-b)[/tex]
[tex](x+2)(x^2-1^2)=0[/tex]
[tex](x+2)(x+1)(x-1)=0[/tex]
Using zero product property, we will get:
[tex](x+2)=0\text{ or }(x+1)=0\text{ or }(x-1)=0[/tex]
[tex]x=-2\text{ or }x=-1\text{ or }x=1[/tex]
Since the zeros of our given function are [tex]-2,-1\text{ and }1[/tex], therefore, options B, C and E are correct choices.
