Question

Without using a calculator determine the number of real zeros of the function f(x) = x^3 + 4x^2 + x -6

Answer 1

Try this:
x³+4x²+x-6=0
1) To re-write the equation into form:
1*x³+4*x²+1*x-6=0, the note 1+4+1=6, it means x=1
2) to re-write the equation into form:
(x-1)(x²+5x+6)=0
(x-1)(x+2)(x+3)=0
3)
$\left[\begin{array}{ccc}x-1=0\\x+2=0\\x+3=0\end{array}\right \ \ \textless \ =\ \textgreater \ \left[\begin{array}{ccc}x=1\\x=-2\\x=-3\end{array}\right$
Answer: -3;-2;1.