Algebra II Note-taking Guide
Algebra II-Lesson 4.03
Please print this out in advance, and as you are working through the lesson, fill in the information and use this as your
notes.
As you complete this lesson, please check that you can answer:
 I know the key features of a polynomial.
 I know how to use the fundamental theorem of Algebra.
 I know how to use the Remainder Theorem.
Learn: pg 1
The Pythagorean Theorem states the ________________of two _____________ of a
___________ triangle is equal to the square of the ___________________________.
Write the Pythagorean in Algebraic form. _____________________________________
What is side C called? ______________________________________
Algebra II Notetaking Guide
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Florida Virtual School
Explain theorem? ______________________________________________________
The Fundamental Theorem of Algebra:
Use the following format for each word. You can use 5 x4 index cards or notebook paper to use
the format below.
Template:
Example:
Vocabulary:
1. Factoring
3. Quadratic formula
2. Discriminate
4. Zeros of function
Explain how you would find the solution to quadratic equations?
If the value of the _________________(b2−4ac) is a ________________ _____________,
then the __________________ ____________________ may be factored.
Algebra II Notetaking Guide
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Florida Virtual School
Example:
x2+11x+18=0
Yes or No
This can be factored
1. look at the GCF – is it greater than 1?
Yes or No
2. look at the discriminate – is it a perfect
square?
x • x equals x2
3. can be factored as _______________?
(
)(
)=0
4. Place the position of the factored
binomial.
Sum of factor is….
( x+ )( x+ ) = 0
5. Now look at the factors for the last
term. That _____________ to the
________________ coefficient of 11.
Write the sum of factors.
x+2 = 0
The zero product property states that in
order for it to be the factor above the
product must be equal to 0. Solve and
show your work.
x+9 = 0
Therefore the solution is….
Algebra II Notetaking Guide
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Florida Virtual School
In order to graph your solution above the y variable will be set equal to zero.
EXAMPLE 1: pg 1
Find the zeros of the function f(x) = (x + 2)(x + 2)(x − 1)(x − 3)
Step 1
Replace the function of f(x) with 0
Step 2
Set each factor equal to zero and
solve for x
Step 3
Identify the zeros of the function
Step 4
Make a graph to confirm the zeros.
Algebra II Notetaking Guide
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Florida Virtual School
Learn: pg 2
The Factor Theorem: to find polynomials that will factor.
Watch the video on pg2 on using synthetic division.
Example 1: pg 2
Is x + 12 a factor of the function f(x) = x2 + 6x − 72? Explain
Learn: pg 3
The Remainder Theorem:
When a function f(x) is in ____________ _____________, the ____________ of the function,
Also known as f(x) = 0, can be found by ___________________each factor equal to
_________ and solving for the ______________________.
The __________________________ Theorem of _________________ tells us the number of
______________ of the _________________ to the degree of the function.
Algebra II Notetaking Guide
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Florida Virtual School
Find how many solutions this function has. Show your work below.
f(x)=x2+11x+18
If the zeros are applied in synthetic division, the ______________ Theorem states that the
remainder will be zero.
Algebra II Notetaking Guide
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Florida Virtual School
Example 1: pg 3
Find the remainder when f(x)=5x2+51x+16 is divided by x+10
Step 1
Using Synthetic Division
Step 2
Using Substitution
Algebra II Notetaking Guide
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Florida Virtual School
Practice: pg 4
Your Try 1 – Find the zeros of each function and show your work
1.
2.
3.
Algebra II Notetaking Guide
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Florida Virtual School
Are you ready?
 Yes, I completed watching the videos on pg 1 and pg2
 Yes, I completed Your Try 1 – 3 on pg 4
 Yes, I completed the Act 1 and Act 2 on pg 5
 Yes, I am ready to take 4.02 assessments
Algebra II Notetaking Guide
Version 14
Florida Virtual School