Question 150029
A zero is where the function touches the x axis or in other words f(x)=0. 
Usually I first graph it to see what's what using EXCEL or graph paper.
{{{ graph( 300, 300, -10, 10, -50, 50, x^3+6x^2-25x+18 )}}}
As you can see it looks like 3 real zeros at x=1, x=2, and x=-9. 
Plug the values into the equation to verify.
x=1
{{{f(x)=x^3+6x^2-25x+18)}}}
{{{f(1)=1^3+6(1)^2-25(1)+18}}}
{{{f(1)=1+6-25+18}}}
{{{f(1)=0}}}
That's a good one.
x=2
{{{f(x)=x^3+6x^2-25x+18)}}}
{{{f(2)=2^3+6(2)^2-25(2)+18}}}
{{{f(2)=8+24-50+18}}}
{{{f(2)=0}}}
That's a good one too.
x=-9
{{{f(x)=x^3+6x^2-25x+18)}}}
{{{f(-9)=(-9)^3+6(-9)^2-25(-9)+18}}}
{{{f(-9)=-729+486+225+18}}}
{{{f(-9)=0}}}
That's a good one too.
You have found all three roots.
You could then represent the function as,
f(x)=(x-1)(x-2)(x+9)