college algebra
posted by niki (help me!) .
for the function g(x)=5x^63x^3+x^2x, list the possible rational zeros of g(x) and then use synthetic division to factor g(x) completely.
***i'm confused, doesn't this problem need a constant?****

sure  it just happens to be zero.
So, factor out the x and see that
g(x)=x(5x^53x^2+x1)
So, now we know 0 is a root, and any other rational roots are ±1/5
So, do a division to see that there are no other rational roots than 0. 
thank you!