Select the complete list of POSSIBLE rational zeros for the polynomial?

Question

p(x)=x^3+3x^2-5x-35

Answer 1

Using Descartes' rule...

1 positive zero
and
2 negative zeros

Answer 2

Rational zeros are all the possible factors of d over all of the possible factors of a, for

p(x) = ax^3 + bx^2 + cx + d

All of the factors of -35 are:
+/- 1, +/- 5, +/- 7, +/- 35

All of the factors of a (which is 1) are:
+/- 1

All possible rational zeros:

+/- (1, 5, 7, 35) / +/- (1)

OR

1, -1, 5, -5, 7, -7, 35, -35

Of course, if neither of these possible rational roots work, it follows that there are irrational and/or complex roots.

Answer 3

x +/- 1: x+/- 5; x +/- 7; x +/- 35