Question 934558
Find the roots.  Factor as much as possible.  Show the exponents as intended in your given polynomial:


f(x) = 3x^5 – 2x^2 + 7x
which looks like this when render tags included
{{{f(x) = 3x^5 – 2x^2 + 7x}}}


Obviously one of the roots will be x=0.
You find the other roots using synthetic division to test the possible roots of -1, -7, -1/3, -7/3, and their opposites.


Be aware, the dividend to start with for synthetic division must include terms with coefficients of 0:
 {{{3x^5+0*x^4+0*x^3–2x^2+7x}}}
----the site's rendering is failing there and I do not know why-------
{{{highlight_green(3x^4+0*x^3+0*x^2-2x+7)}}}, THIS is the dividend to start with, since you would factorize the common x from the original polynomial.


I did not complete the whole process for you.  I only explained how to start.