Question

What are the real zeros of the function g(x)=x^3+2x^2-x-2

Answer 1

$g(x)=x^3+2x^2-x-2\\\\\text{The zeros:}\\\\g(x)=0\to x^3+2x^2-x-2=0\\\\x^2(x+2)-1(x+2)=0\\\\(x+2)(x^2-1)=0\iff x+2=0\ \vee\ x^2-1=0\\\\x+2=0\ \ \ |-2\\x=-2\\\\x^2-1=0\ \ \ |+1\\x^2=1\to x=\pm\sqrt{1}\to x=-1\ \vee\ x=1\\\\\text{Answer:}\ x=-2\ or\ x=-1\ or\ x=1$