Answer
$5,-5,-4$
Work Step by Step
Given: $x^3+4x^2-25x-100=0$
or, $x^2(x+4)-25(x+4)=0$
Need to use factorization to solve the quadratic equation.
This can be factorized as follows:
$(x^2-25)(x+4)=0$
or, $(x-5)(x+5)(x+4)=0 $
Now, $x-5=0$ , and $x+5=0$ and $x+4=0$
This implies $x=5,-5,-4$
