2.5 Zeros of Polynomial Functions The Rational Zero Theorem Possible rational zeros = Provides us with a list of all possible rational zeros of a polynomial function. Factors of the constant Factors of the l.c. 1
List all possible rational zeros of f(x) = x3 + 3x2 – 6x – 8 Example List all possible rational zeros of f(x) = x3 + 3x2 – 6x – 8 You try one List all possible rational zeros of f(x) = x3 + 2x2 – 5x – 6 2
List all possible rational zeros of f(x) = 3x4 – 11x3 – 3x2 – 6x + 8 Example List all possible rational zeros of f(x) = 3x4 – 11x3 – 3x2 – 6x + 8 You try one List all possible rational zeros of f(x) = 4x5 + 12x4 –x – 3 3
Combining the list with synthetic division will allow us to solve a function. Example Find all zeros of f(x) = x3 – 2x2 – 11x + 12 4
You try one Find all zeros of f(x) = x3 + 8x2 + 11x – 20 5
P. 335 #1 – 15 odd 6