1. 2.6 – Find Rational zeros
Coach Bianco

2. 2.6 – Find Rational zeros
Georgia Performance Standards:
MM3A3a – Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.
MM3A3d – Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

3. Find zeros when the leading coefficient is 1
Find all real zeros of f(x) = x3 – 7x2 + 14x – 8. *The rational root theorem states if anxn + … + a1x + a0 has integer coefficients, then every rational zero of f has the form =

4. Find zeros when the leading coefficient is 1
Find all real zeros of f(x) = x3 – 7x2 + 14x – 8
Steps:
List the possible rational zeros. The leading coefficient is 1 and the constant term is -8. The possible real zeros are: x = +- 1, +-2, +-4, +- 8
Test these zeros using synthetic division. Test x = 4: 4
*Because 4 is a zero of f(x) = (x -4)(x2 – 3x + 2).
4 is a zero

5. Find zeros when the leading coefficient is 1
Find all real zeros of f(x) = x3 – 7x2 + 14x – 8
Steps:
List the possible rational zeros. The leading coefficient is 1 and the constant term is -8. The possible real zeros are: x = +- 1, +-2, +-4, +- 8
Test these zeros using synthetic division. Test x = 4:
Factor the trinomial and use the factor theorem.
f(x) = (x -4)(x2 – 3x + 2) = (x – 4)(x – 2)(x – 1)
The zeros are 1, 2, and 4.

6. Find zeros when the leading coefficient is not 1
Find all real zeros of f(x) = 3x3 – 17x2 + 18x + 8.
Steps:
List the possible rational zeros
Choose a reasonable value to check using the graph of the function
Check with synthetic division
Factor out a binomial using the result of synthetic division

7. Find zeros when the leading coefficient is not 1
Find all real zeros of f(x) = 3x3 – 17x2 + 18x + 8. Possible zeros: +- 1, 2, 4, 8, - -
is a zero

8. Find zeros when the leading coefficient is not 1
Find all real zeros of f(x) = 3x3 – 17x2 + 18x + 8.
Steps:
List the possible rational zeros
Choose a reasonable value to check using the graph of the function
Check with synthetic division
Factor out a binomial using the result of synthetic division

9. Find zeros when the leading coefficient is not 1
Find all real zeros of f(x) = 3x3 – 17x2 + 18x + 8. *The real zeros are , 2, and 4. -

10. Guided practice: Page 90 (1-6)