precal question

Question

List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros). (Enter your answers as a comma-separated list.)

R(x) = 2x⁵ + 6x³ + 3x² − 6

Answer 1

The rational zeros theorem says that all possible rational (numbers that can be written as fractions) zeros, or x-intercepts, of a polynomial may be found by putting all the factors of the constant over the factors of the leading coefficient.

The constant here is -6, and the leading coefficient is 2.

6 has the factors 1, 2, 3, and 6. 2 only has 1 and 2. Using the positive and negative versions of each fraction, the possibilities are:

± {1/1, 1/2, 2/1, 2/2, 3/1, 3/2, 6/1, 6/2}.

Eliminating the fractions that simplify to the same values, we have ±{1, 1/2, 2, 3, 3/2, 6}.

I hope that helps!

Let me know if you have any questions, and have fun! Pre-calc is awesome!

Liz Z.