It's an introduction to polynomials with an explanation of The Remainder Theorem and The Factor Theorem for Class 10 students. It has some questions for the explanation of the concepts
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
2. A polynomial looks like this:
INTRODUCTION
A polynomial has:
Variables such as x,y,z with powers as whole
numbers(0,1,2,3…)
Constants like 10
3. 1. Monomial = The polynomial with only one
term. E.g. -2x,5y
2. Binomial = The polynomial with two terms.
E.g. 3x3+5x, 6y+5
3. Trinomial = The polynomial with three terms.
E.g. 4x4+3x2+2, 5y3+4y+9
Types of polynomials
4. When we know the degree we can also give the
polynomial a name:
The Degree of a Polynomial with
one variable is ...
... the largest exponent of that
variable.
DEGREE OF A POLYNOMIAL
6. WAYS TO FIND ZEROES
1. Graphically
Example: 2x+1
2x+1 is a linear polynomial:
The graph cuts the x-axis at -1/2
which means that at this point
the value of the function y=2x+1
is 0
. Basic Algebra
Example: 2x+1
A "root" is when y is zero: 2x+1 = 0
Subtract 1 from both sides: 2x = −1
Divide both sides by 2: x = −1/2
And that is the solution:
x = −1/2
7. Do you remember doing
division in Arithmetic?
"7 divided by 2 equals 3 with a remainder of 1"
Well, we can divide polynomials in a similar manner
Remainder
Theorem
8. POLYNOMIAL DIVISION EXAMPLE
Example: 2x2−5x−1 divided by x−3
f(x) is 2x2−5x−1
d(x) is x−3
After dividing we get the answer 2x+1, but there is a remainder
of 2.
q(x) is 2x+1
r(x) is 2
In the style f(x) = d(x)·q(x) + r(x) we can write:
2x2−5x−1 = (x−3)(2x+1) + 2
You may refer to our another video “Long
Division Method” to see detailed
explanationKeep in
mind
9. The Remainder Theorem
The Remainder Theorem:
When we divide a polynomial f(x) by x−c the remainder is f(c)
When we divide f(x) by the simple polynomial x−c we get:
f(x) = (x−c)·q(x) + r(x)
x−c is degree 1, so r(x) must have degree 0, so it is just some
constant r :
f(x) = (x−c)·q(x) + r
Now see what happens when we have x equal to c:
f(c) =(c−c)·q(c) + r
f(c) =(0)·q(c) + r
f(c) =r
This is the basis of
remainder theorem…
10. Let’s understand with an example
So to find the remainder after dividing by x-c we don't
need to do any division:
Just find f(c)
We didn't need to
do Long Division at
all!
12. The Factor
Theorem
Now ...
We see this when dividing whole numbers. For example 60 ÷ 20
= 3 with no remainder. So 20 must be a factor of 60.
The Factor
Theorem:
When f(c)=0 then x−c
is a factor of f(x)
And the other way
around, too:
When x−c is a factor
of f(x) then f(c)=0