Respuesta :

Answer:

Option A: [tex]x=0[/tex], [tex]x=-2[/tex], and [tex]x=-4[/tex]

Step-by-step explanation:

[tex]f(x)=x^3+6x^2+8x[/tex]

[tex]0=x^3+6x^2+8x[/tex]

[tex]0=x(x^2+6x+8)[/tex]

[tex]0=x(x+2)(x+4)[/tex]

[tex]x=0[/tex], [tex]x=-2[/tex], and [tex]x=-4[/tex]

loneguy

[tex]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[/tex]

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