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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.
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
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
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
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

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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