Given the equation:
[tex]g(x)=x^3+6x^2+8x[/tex]To find the zeros of the graph, we will solve the equation: g(x) = 0
so,
[tex]x^3+6x^2+8x=0[/tex]Factor the equation to find the values of x:
[tex]\begin{gathered} x(x^2+6x+8)=0 \\ x(x+2)(x+4)=0 \\ x=0 \\ or,(x+2)=0\rightarrow x=-2 \\ or,(x+4)=0\rightarrow x=-4 \end{gathered}[/tex]so, the answer will be the zeros of the function are:
[tex]x=\mleft\lbrace-4,-2,0\mright\rbrace[/tex]
