Bell Work
1. A degree 5 polynomial has exactly 5 ________
zeros.
2. A degree 5 polynomial has no more than 5
_______ zeros.
3. Only real zeros are also ______________.
2.4-2.5 Quiz Topics to Know
•
•
•
•
•
•
•
•
•
•
•
Long Division
Synthetic Division
Remainder Theorem
Factor Theorem
Rational Zeros Theorem
Upper Bound/Lower Bound Theorems
Fundamental Theorem of Algebra
Linear Factorization Theorem
Complex Conjugate Zeros Theorem
Complex vs. Real Zeros
Find all zeros/write the linear factorization or standard form
Quiz Review
1. Use synthetic division to determine if 2 is an
upper bound for the real zeros of
f(x) = x4 – x3 + x2 + x – 12.
Quiz Review
2. Use the factor theorem to determine if x – 3 is
a factor of f(x) = x3 – 3x2 + 2x - 3
Quiz Review
3. Divide f(x) = x4 - 2x3 + 3x2 – 4x + 6 by
d(x) = x2 + 2x - 1 using long division.
Quiz Review
4. Divide f(x) = x3 – 5x2 – 2 by x + 1 using
synthetic division.
Quiz Review
5. Use synthetic division to determine if -1 is a
lower bound for the real zeros of
f(x) = 4x3 – 5x2 + 2x + 20.
Quiz Review
6. Use the Rational Zeros Theorem to write a list
of all the possible rational zeros of
f(x) = 4x4 + 10x2 + 5x + 3
Quiz Review
7. Match the zeros and multiplicities of the
polynomial function to the graph.
(a)
(b)
(c)
(d)
-4 (multiplicity 2), 1 (multiplicity 3)
-4 (multiplicity 3), 1 (multiplicity 2)
-4 (multiplicity 2), 1 (multiplicity 2)
-4 (multiplicity 3), 1 (multiplicity 3)
Quiz Review
8. Write a polynomial function whose zeros
include those listed below.
(linear factorization vs. standard form)
-4, 5, 2 + 3i
Quiz Review
9. State how many complex and real zeros the
function has.
𝑓 𝑥 = 𝑥 4 − 2𝑥 2 + 3𝑥 − 4
Quiz Review
10. Find all of the real zeros of the function.
(give exact values not decimals)
And write the linear factorization of the function.
f(x) = x3 – 6x2 + 7x + 4
Quiz Review
11. Find all of the real zeros of the function.
(give exact values not decimals)
And write the linear factorization of the function.
f(x) = 2x3 – 3x2 - 4x + 6