1. 5.6 Find The Rational Zeros
Zeros is another word for solutions.

2. List Possible Rational Zeros
Use p/q to find the possible rational zeros.
p represents the factors of the constant term
q represents the factors of the leading coeff.
(EX) x3 + 2x2 – 11x + 12
p = factors of 12 (constant term)
q = factors of 1 (leading coefficient)
Make a list of all the possible combinations of
p/q.

3. List the possible zeros of the polynomial below:
(EX) f(x) = 4x4 – x3 – 3x2 + 9x – 10
(EX) f(x) = x3 + 9x2 + 23x + 15
(EX) f(x) = 2x3 + 3x2 – 11x – 6

4. Find zeros when the leading coefficient is 1.
Step 1: List the possible rational zeros. p/q
Step 2: Test the zeros using synthetic division.
Use the possible factors as the substitution number until you get a remainder of 0.
Step 3: Factor the trinomial and solve for x.

5. Find the zeros: (EX) f(x) = x3 – 8x2 + 11x + 20

6. Find zeros when the leading coefficient is not 1.
(EX) f(x) = 10x4 – 11x3 – 42x2 + 7x + 12
Step1: List the possible p/q
Step2: Choose reasonable numbers by viewing the graph.
Step3: Check the reasonable numbers using synthetic division
Step4: Factor the polynomial.
Step5: Repeat the steps above with the new polynomial

7. Practice Problem: Find the zeros of the function:
(EX) 2x4 + 5x3 – 18x2 – 19x + 42

8. CW/HW
Page 374 (3,5,7,11,13,24)