precalculus
posted by Sara .
I'm going to do this on my own, but I would like to check mine against yours  give me today to work on it and I will be able to compare. List all possible rational zeros for the polynomial find all real zeros and factor completely. show work
f(x)=3x^429x^3+89x^275x36
thank you.

good for you
Tried x + ±1, ± 2, ±3
found f(3) = 0
so by synthetic division
(x3)(3x^3  20x^2 + 29x + 12)
found x = 4 works in 2nd bracket, so x4 is a factor
another synthetic division .....
so far
(x3)(x4)(3x^2  8x  3)
and the quadratic factored again
= (x3)9x4(x3)(3x + 1)
= (x4)(3x+1)(x3)^2 , double root at x=3
so x =  1/3, 3, 4