For the function $g(x) = x^{3} + x^{2} − 6x$, find the value of each expression below.

5. Find at least one value of $x$ for which $g(x) = 0$.

   Hint (e):

   Let $g(x) = 0$ in the original equation and then solve for $x$.

   Steps (e):

   $0=x^3+x^2-6x$
   $0=x(x^2+x-6)$
   $0=x(x+3)(x-2)$

   Answer (e)

   $x = −3$, $0$, $2$

6. If $f(x) = x^{2} − x + 3$, find $g(x) − f(x)$.

   Step 1(f):

   $g(x) − f(x) = \left(x^{3} + x^{2} − 6x\right) − \left(x^{2} − x + 3\right)$

   Step 2 (f):

   Remove parentheses. Pay attention to the minus sign in front of $f(x)$. Combine like terms.