Finding the X- Intercepts for this Equation How do you find the x intercepts for this problem? (Please show and explain how you solved it)

$$y= x^3-10x^2+31x-30$$
Another method is this:  if $$x^3+ax^2+bx+c=0$$ then you are looking to solve the following system.

$$r+s+t=a$$
$$rs+rt+st=b$$
$$rst=c$$

Should you find these $r,s,t$, these are your roots and your factored polynomial is just 

$$(x-r)(x-s)(x-t)=0$$

However, not knowing these formulas is probably true.  In this case use the rational root theorem.  Test the possible rational roots (the factors of 30 in your case, $c$ in the general case) and then divide by the root or factor with long division or synthetic.  

For your example, your possible rational roots are $1,2,3,5,6,10,15,30$.  You test both positive and negative factors.  You would find your first bit of luck with $2$ (the factor being $x-2$)...when you divide you will get a quotient of $x^2-8x+15$.  Then factor that.  See reckless reckoner's comment for further insight.
For X intercepts we have y=0 as shown in fig .You just have to findroots of polynomial .Thanks