Alg2 lesson 7-6
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The Rational Number Theorem states that if a polynomial function has integer coefficients, any rational zero must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. This document provides examples of finding the possible rational zeros of polynomial functions by listing the factors of the constant and leading coefficients. It determines the actual zeros of the function 2x^3 + 3x^2 - 8x + 3 to be 1, 1/2, and -3.
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Alg2 lesson 7-6
- 1. Rational Number Theorem: If a polynomial function, written in descending order, has integer coefficients, then any rational zero must be of the form ± p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
- 2. List all of the possible rational zeros of Factors of 4: 1, 2, 4 Factors of 3: 1 , 3 1 1 2 2 4 4 1 3 1 3 1 3
- 3. List all of the possible rational zeros of Factors of 6: 1, 2, 3, 6 Factors of 2: 1 , 2 1 1 2 2 3 3 6 6 1 2 1 2 1 2 1 2
- 4. Find all zeros of the function f(x) = 2x3 + 3x2 – 8x + 3 What are the possible rational zeros? Factors of 3: 1, 3 Factors of 2: 1, 2 Possible zeros : 1 , 1 , 3 , 3 1 2 1 2
- 5. Find all zeros of the function f(x) = 2x3 + 3x2 – 8x + 3 Possible zeros : 1 , 1 , 3 , 3 1 2 1 2 2 3 -8 3 2x2 + 5x - 3 = 0 1 2 5 -3 (2x - 1)(x + 3) = 0 2 5 -3 0 x = 1/2 x = -3 Zeros: 1, 1/2, -3