Determine the number of possible positive and negative real zeros for the given function

Question

I made it this far and now I am thrown off with this part

v(-x)= -x^5+9x^4+5x^3+6x^2+4x+7

Number of possible positive real zeros

Number of possible negative real zeros

Number of nonreal zeros

Total(including multiplicities)

Answer 1

Any 5th degree equation has 5 zeroes

they would have 1, 3 or 5 real zeroes

with 2 or 4 possible imaginary zeroes

plug in a few simple integers to sketch part of the graph

and you see a local minimum near =-1/3 and a positive real zero between x=6 and 7

Odds are there's 4 imaginary zeroes and one positive real zero, and zero negative zeroes..

with very large or very negative x values, the 5th degree term dominates. The graph

definitely crosses the x axis with a positive x value

If you can't factor the polynomial or it's derivative, about all you can do is sketch the graph

or use a graphing calculator.