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? ______
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 / 2. Discriminate3. Quadratic formula / 4. Zeros of function
Explain how you would find the solution to quadratic equations?
If the value of the ______(b2−4ac)is a ______,
thenthe ______may be factored.
Example:
x2+11x+18=0 / This can be factoredYes or No / 1. look at the GCF – is it greater than 1?
Yes or No / 2. look at the discriminate – is it a perfect square?
x•xequalsx2 / 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
x+9 / = / 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.
Therefore the solution is….
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 0Step 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.
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.
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.
Example 1: pg 3 Find the remainder whenf(x)=5x2+51x+16is divided byx+10
Step 1 / Using Synthetic DivisionStep 2 / Using Substitution
Practice: pg 4
Your Try 1 – Find the zeros of each function and show your work
1.
2.
3.
Are you ready?
Yes, I completed watching the videos on pg1 and pg2
Yes, I completedYour Try 1 – 3 on pg 4
Yes, I completed the Act 1 and Act 2 on pg 5
Yes, I am ready to take 4.02assessments
Algebra II Notetaking Guide
Version 14
Florida Virtual School