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