Question

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.f(x) = 3x3 + 39x2 + 39x + 27

Answer 1

First, we can factor this to make it easier to solve:

3(x^3 + 13x^2 + 13x + 9)

Now, we can use the rational root theorem like so:

List factors of 9:

1, 3, 9.

List factors of 1:

1

Because of this, we know our possible rational roots are:

+/-1, +/-3, +/-9

If none of these zeros fit using the remainder theorem, then we know our roots will be irrational.