Question

What are the zeros of the polynomial function? f(x)=x3+2x2−x−2 Select each correct answer. A.−3 B. −2 C. −1D. 0 E. 1F. 2 G. 3

Answer 1

-2

-1

1

Explanation:

Answer 2

B. −2

C. −1

E. 1

Explanation:

He have been given a polynomial function
`f(x)=x^3+2x^2-x-2`. 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:

`x^3+2x^2-x-2=0`

Now, we will factor our equation by grouping method.

`(x^3+2x^2)-(x+2)=0`

`x^2(x+2)-1(x+2)=0`

`(x+2)(x^2-1)=0`

Now, we will use difference of squares
`a^b-b^2=(a+b)(a-b)`

`(x+2)(x^2-1^2)=0`

`(x+2)(x+1)(x-1)=0`

Using zero product property, we will get:

`(x+2)=0\text{ or }(x+1)=0\text{ or }(x-1)=0`

`x=-2\text{ or }x=-1\text{ or }x=1`

Since the zeros of our given function are
`-2,-1\text{ and }1`, therefore, options B, C and E are correct choices.