Question

What does the rational zero theorem help determine for the polynomial f(x)=3x³−2x²+5x−9?

(a) The degree of the polynomial
(b) The possible rational zeros
(c) The coefficient of the leading term
(d) The sum of all zeros

Answer 1

The rational zero theorem helps determine the possible rational zeros for a polynomial. To find the possible rational zeros of the polynomial f(x)=3x³−2x²+5x−9, we look at the factors of the constant term (-9) divided by the factors of the leading coefficient (3).

Step-by-step explanation:

The rational zero theorem helps determine the possible rational zeros for a polynomial. To find the possible rational zeros of the polynomial f(x)=3x³−2x²+5x−9, we look at the factors of the constant term (-9) divided by the factors of the leading coefficient (3). We can use the rational zero theorem to generate a list of possible rational zeros, which can then be tested using synthetic division or substitution.