Question

Find the zeros of ƒ(x) = x3 + 6x2 + 8x.

A) x = 0, –2, –4
B) x = 0, 2, 4
C) x = 2, 4
D) x = –2, –4

Answer 1

Option A:
`x=0`,
`x=-2`, and
`x=-4`

Explanation:

`f(x)=x^3+6x^2+8x`

`0=x^3+6x^2+8x`

`0=x(x^2+6x+8)`

`0=x(x+2)(x+4)`

`x=0`,
`x=-2`, and
`x=-4`

Answer 2

`x^3+6x^2+8x = 0\\\\\implies x^3+2x^2 +4x^2+8x =0\\\\\implies x^2(x+2) +4x (x+2) =0\\\\\implies (x+2)(x^2 +4x) = 0\\\\\implies x (x+2) (x+4)=0\\\\\text{Hence,} \\\\x = 0 ,-2,-4`