Question

Extended response question? Please help me? :(

Answer 1

Using complete sentences, describe how you would find all possible rational zeros of the polynomial function f(x) = 9x^4 – 17x^3 + 2x^2 – 3x + 33.

Answer 2

Polynomial functions with integer coefficients have roots = p/q
where p = factor of constant (33)
and q = factor of leading coefficient (9)

Possible values for p: ±1, ±3, ±11, ±33
Possible values for q: 1, 3, 9

NOTE: I don't bother with negative values for q, since I already have positive and negative values for p. So letting p = 11 and q = -1 is the same as letting p = -11 and q = 1.

So all possible rational roots are
±1, ±1/3, ±1/9, ±3, ±11, ±11/3, ±11/9, ±33

Trying all these possible values of x, we find that none is a zero of f(x)
(It would be helpful to have a programming calculator, enter the function, then enter each value of x)