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# Alg2 lesson 7-6

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### Alg2 lesson 7-6

1. 1. Rational Number Theorem:If a polynomial function, written indescending order, has integercoefficients, then any rational zero mustbe of the form ± p/q, where p is a factor ofthe constant term and q is a factor of theleading coefficient.
2. 2. List all of the possible rational zeros ofFactors of 4: 1, 2, 4Factors of 3: 1 , 3 1 1 2 2 4 4 1 3 1 3 1 3
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. 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. 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