list all the possible rational zeros for the polynomial below. find all the zeros of the polynomialbelow and factor completely.

F(x)=5x^4-x^3-33x^2-43x-16

1 answer

possible rational roots will have numerator 1,2,4,8,16 (or negatives)
denominator 1 or 5 (or negatives)

A little synthetic division reveals thet

F(x) = (x+1)^3 * (5x -16)