Question

What are the zeros of the polynomial function

F(x) = x3 + x2 - 6x?
A. x= -3, x = 0, and x = 2
B. x = -2, x = 0, and x = 3
C. x= -1, x = 0, and x = 6
D. x= -6, x = 0, and x = 1

Answer 1

x=0, x= -3 and x=2

Explanation:

`f(x)=x^3+x^2-6x`

put f(x)=0

`f(x)=0`

`x^3+x^2-6x=0`

`x(x^2+x-6)=0`

Splitting the middle term in such a way that their product is
`-6x^2` and sum is
`x`

`x(x^2+3x-2x-6)=0`

`x[x(x+3)-2(x+3)]=0`

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

hence

`x=0`

`(x+3)=0`

`x=-3`

`(x-2)=0`

`x=2`

hence the zeros of the polynomial are 0,-3,2