3-4 Factoring Polynomials - Part 1
Presentation
•
Mathematics
•
9th - 12th Grade
•
Medium
Kathleen Cavanagh
Used 3+ times
FREE Resource
31 Slides • 13 Questions
1
3-4 Factoring Polynomials - Part 1
2
3-4 Notes Part 1 - factoring polynomials
3
Multiple Choice
If one number is divisible by another, what should be the remainder if you were to divide them?
1
0
undefined
2
4
This also applies when dividing polynomials!
(yeah!)
5
Multiple Select
How can you tell if (x-5) is a factor of x3-125? Select all that apply.
Divide. If the remainder is 0 then (x-5) is a factor.
Divide. If the remainder is 1 then (x-5) is a factor.
Use the remainder theorem by plugging in 5. If the remainder is 0 then (x-5) is a factor.
Use the remainder theorem by plugging in -5. If the remainder if 0 then (x-5) is a factor.
6
Multiple Choice
Is (x-5) a factor of x3-125?
Yes
No
7
8
We can use division to factor polynomials of higher degrees
9
In the previous example, (x3-125)÷(x-5) = x2+5x+25.
Working backwards, that means multiplying (x2+5x+25) and (x-5) is equal to x3-125.
10
11
If x2+5x+25 was factorable, we would keep factoring.
Since it's not, the expression is factored completely.
12
Multiple Choice
One factor is x-3. Find the other factor of
x3−x2−10x+24
x2−x−10+x−324
x3+5x2+2x
x2+5x+2
13
Since you were told x-3 is a factor, you know the remainder has to be 0. If it isn't, you made a mistake somewhere.
Woops!
14
Multiple Choice
Select the factored form of
p(x)=x3+2x2−13x−6(x−3)(x3−x2−10x+24)
(x−3)(x3+5x2+2x)
(x−3)(x2−x−10+x−324)
(x−3)(x2+5x+2)
15
Fill in the Blanks
Type answer...
16
Multiple Select
Review:
Now solve by factoring.
x2-8x-20=0
10
2
-2
-10
17
Remember, to solve by factoring, set each factor equal to 0 and solve for x.
- x-10=0
- Add 10 to get x=10
- x+2=0
- Subtract 2 to get x=-2
18
Read this problem. I will go through it one step at a time.
19
20
Multiple Choice
What year will the pond dry up?
2016
2010
2030
2006
21
The problem states that the water level of the pond has been measured since 2006. That means the y-intercept is the water level in 2006. The pond's depth reaches 0 feet at an x-value of 10. Since x is years, 10 years since 2006 would be the year 2016.
22
It actually is fun!
23
24
25
26
That means we can divide x3-16x2+74x-140 by x-10 and get a remainder of 0.
27
Multiple Choice
Use synthetic division to divide(x3−16x2+74x−140)÷(x−10)
x2−6x+14
x3−6x2+14x
x2−26x+334−x−103480
x2−26x+334−x+103480
28
29
This is the fully factored form of d(x)
30
The amount of voters on a single day is represented by the graph, where x is hours and y is number of voters.
31
We can tell a lot about this scenario just by looking at the graph.
32
Approximately how many voters arrived when the voting location opened? Go to the next slide to answer.
33
Multiple Choice
Approximately how many voters arrived when the voting location opened?
56
8
4
26
34
Since we can't have negative time, 0 hours is when the voting location opens. The y-value is 56.
35
Approximately how many voters were there 2.6 hours after opening? Go to the next slide to answer.
36
Multiple Choice
Approximately how many voters were there 2.6 hours after opening?
10
26
4
34
37
About 2.6 hours, the y-value is approximately 4.
38
How long is this polling place open? Go to the next slide to answer.
39
Multiple Choice
How long is this polling place open?
8 hours
6.1 horus
2.6 hours
4.7 hours
40
The number of people becomes negative after 8 hours, which doesn't make sense.
41
The equation of the graph is undefined
42
Multiple Choice
p(x)=−x3+13x2−47x+56 Use the graph to factor p(x)
(x2−5x+7)(x−8)
−1(x2−5x+7)(x−8)
−1(x+8)(−x3+21x2−215)
−1(x+8)(x2+21x−215)
43
44
Make sure you also complete 3-4 Notes Part 2!
3-4 Factoring Polynomials - Part 1
Show answer
Auto Play
Slide 1 / 44
SLIDE
Similar Resources on Wayground
38 questions
Logarithms Afterview
Presentation
•
9th - 12th Grade
39 questions
Weeks 27/28 Transformations
Presentation
•
9th - 12th Grade
40 questions
French subjunctive mood
Presentation
•
9th - 12th Grade
38 questions
Tangent Properties
Presentation
•
9th - 12th Grade
39 questions
Lesson 48 Fall 2022 Parallel Lines and Transversals
Presentation
•
9th - 12th Grade
37 questions
Lesson 4.07 Characteristics of Quadratic Functions
Presentation
•
9th - 12th Grade
38 questions
Unit 4- Lesson 4: Elections
Presentation
•
9th - 12th Grade
38 questions
Chemical Reactions - Types of Reactions
Presentation
•
9th - 12th Grade
Popular Resources on Wayground
24 questions
PBIS-HGMS Day 10
Quiz
•
6th - 8th Grade
10 questions
HCS SCI 03 Summer School Review 3
Quiz
•
3rd Grade
11 questions
Home Scope
Quiz
•
7th - 8th Grade
15 questions
HCS SCI 05 Summer School Assessment 3 Review
Quiz
•
5th Grade
35 questions
Lufkin Road Middle School Student Handbook & Policies Assessment
Quiz
•
7th Grade
18 questions
Geo 11.3 Area of Circles and Sectors
Quiz
•
9th - 11th Grade