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. The document provides examples of finding all possible rational zeros of polynomial functions by listing the factors of the constant and leading coefficients. It demonstrates finding the actual zeros of a function by factoring the polynomial and setting each factor equal to zero.
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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 ofFactors of 4: 1, 2, 4Factors of 3: 1 , 31122441 3 1 3 1 3 Example 6-1a
- 3. List all of the possible rational zeros of Factors of 6: 1, 2, 3, 6Factors of 2: 1 , 2112233661 2 1 2 1 2 1 2 Example 6-1c
- 4. Find all zeros of the function f(x) = 2x3 + 3x2 – 8x + 3What are the possible rational zeros? Factors of 3: 1, 3Factors of 2: 1, 2Possible zeros : 1 , 1 , 3 , 3 1 2 1 2
- 5. Find all zeros of the function f(x) = 2x3 + 3x2 – 8x + 3Possible zeros : 1 , 1 , 3 , 3 1 2 1 2 2 3 -8 31 2 5 -3 2 5 -3 02x2 + 5x - 3 = 0(2x - 1)(x + 3) = 0x = 1/2 x = -3Zeros: 1, 1/2, -3