Download Warm Up - bishopa-ALG3

Warm Up
•
•
•
•
•
Find the degree and leading coefficient
1. 𝑥 3 + 3𝑥 2 + 16𝑥 + 48
2. −4𝑥 7 + 2
3. −𝑥 4 − 5𝑥 2
4. 5𝑥 − 3
Algebra 3
Chapter 6
Lesson 7: Using the
Fundamental
Theorem of Algebra
VOCAB
• The Fundamental Theorem of Algebra – if
𝑓(𝑥) is a polynomial of degree n where n > 0
then 𝑓 𝑥 = 0 has at least one root in the set
of complex numbers
• Repeated Solution – is when you have the
same answer twice (this comes from a square)
– Ex (𝑥 − 2)2
GOAL
• Today you will be able to find how many total
zeros a problem has.
– This is different than last week.
– Last week was REAL zeros
• Today will include imaginary
Directions (Number of Solutions/ Zeros)
• Write the problem in standard form
• Look at the degree (that’s your answer)
I DO (Number of Solutions/ Zeros)
• Find how many solutions/zeros the
polynomial has.
• 1. 𝑥 3 + 3𝑥 2 + 16𝑥 + 48 = 0
• 2. 𝑥 4 + 6𝑥 3 + 12𝑥 2 + 8𝑥
• 3. 𝑥 3 − 3𝑥 2 + 4𝑥 + 2 = 0
• 4. 5𝑥 − 7
WE DO (Number of Solutions/ Zeros)
• Find how many solutions/zeros the
polynomial has.
• 1. 𝑥 19 − 2𝑥 4 − 2 = 0
• 2. −𝑥 4
• 3. 7𝑥 21 + 13𝑥 12 − 32 = 0
• 4. 4
YOU DO (Number of Solutions/ Zeros)
• Find how many solutions/zeros the
polynomial has.
• 1. −2𝑥 31 + 7𝑥 24 − 13𝑥 + 4 = 0
• 2. 9𝑥 164 + 64𝑥 314 + 13𝑥 2128 + 8𝑥
• 3. -3𝑥 123 − 3𝑥 456 + 4𝑥 = 0
• 4. 17𝑥
REVIEW
• What did you just learn?
Homework
• Worksheet
– 6.7B (1 – 4)
Directions (Identifying Factors)
• Numbers
– Take the opposite
– Write (x ____ )
• Complex Numbers
– You need to take both
• 𝑎 + 𝑏𝑖
• 𝑎 − 𝑏𝑖
– Write (x –(𝑎 + 𝑏𝑖)) or (x –(𝑎 − 𝑏𝑖))
I DO (Identifying Factors)
• Identify the factors of a polynomial function
that has the given zeros
• 1. 3, 0, -2
• 2. 1, 1, i, -i
• 3. 5, 2 + 3i
• 4. 1, -1, 2, -2, 3
WE DO (Identifying Factors)
• Identify the factors of a polynomial function
that has the given zeros
• 1. 3, -2, -1 + i
• 2. 4i, 4i
• 3. -4, 5, 5
• 4. -3, 4i, -4i
Warm Up
• Find how many solutions/zeros the
polynomial has.
• 1. 13𝑥 + 4 = 0
• 2. 9𝑥 14 + 64𝑥 34 + 13𝑥 79 + 8𝑥
• 3. -4𝑥 215 + 3𝑥 251 − 7 = 0
• 4. 17
TODAY
• We will learn how to identify factors of a
polynomial and write a polynomial function
from the zeros
WE DO (Identifying Factors)
• Identify the factors of a polynomial function
that has the given zeros
• 1. -2, -2, -2, 0
• 2. 6
• 3. 3, 5 - i
• 4. -4, -4, 2i, -2i
YOU DO (Identifying Factors)
• Identify the factors of a polynomial function
that has the given zeros
• 1. 3, 0, -i
• 2. 5, 5, -4 - i
• 3. -6, 2, 1, 1
• 4. 5i, 2, 3 - 2i
REVIEW
• Today we learned how to identify the factors
of a polynomial function when given the zeros
HOMEWORK
• Worksheet
– 6.7B (9 - 14)
DIRECTIONS (Writing Polynomials)
• Identify the factors
• Simplify
– FOIL
– Combine Like Terms
Warm Up
• Identify the factors of a polynomial function
that has the given zeros
• 1. 2, -3, 4i, 5 - i
I DO (Writing Polynomials)
• Write a polynomial function of least degree that has
real coefficients, the given zeros, and a leading
coefficient of 1
• 1. 6
• 2. -3 , 5
• 3. 3 + 4i, 0
• 4. 2 – i, 1 , 2
WE DO (Writing Polynomials)
• Write a polynomial function of least degree
that has real coefficients, the given zeros, and
a leading coefficient of 1
• 1. -1, 1, 3
• 2. 2, 3, 0
• 3. 5 -2i, i, 0, 3
• 4. 2i, -2i, 5i, -5i
YOU DO (Writing Polynomials)
• Write a polynomial function of least degree
that has real coefficients, the given zeros, and
a leading coefficient of 1
• 1. 0, 3, -4
• 2. -2, 1
• 3. 4 + i, 4 – i, -2
• 4. 3i, 2, -4
Review
• What did you learn?
Homework
• Worksheet
– 6.7B (15 – 23)
WARM UP
•DO NOT TURN IN
YOUR HOMEWORK
•Write the equation
• 1. 2, 0, 3, -1
TODAY
• We will review writing polynomial equations
when given the zeros
Remember
• Quiz Tomorrow
• Make a cheat sheet