Given the function:
[tex]f(x)=x^3+5x^2+2x-8[/tex]
We know that x = 1 is a zero of the polynomial, so taking the division:
Then, we can rewrite the polynomial as:
[tex]f(x)=(x-1)(x^2+6x+8)[/tex]
Now, for the quadratic term:
[tex]x^2+6x+8=(x+2)(x+4)[/tex]
Then:
[tex]f(x)=(x-1)(x+2)(x+4)[/tex]
Finally, the other zeros of the function are:
[tex]\begin{gathered} x+2=0\Rightarrow x=-2 \\ x+4=0\Rightarrow x=-4 \end{gathered}[/tex]
