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Saint Mary’s Angels College of Pampanga
COLLEGE OF EDUCATION
Sta. Ana, Pampanga
A DETAILED LESSON PLAN
IN MATHEMATICS 10
I. Objectives
At the end of the lesson, 90% the students must be able to attain the following objectives
with 75% accuracy:
A. Define Polynomial Functions.
B. Illustrate Polynomial Functions.
C. Identify leading term, leading coefficient, degree and the constant term.
II. Subject Matter
Topic: Polynomial Function (M10AL-IIa-1)
Reference: k-12 Conceptual Math & Beyond 10
Instructional Materials: PowerPoint presentation, Laptop, and Projector
III. Procedure
Teacher’s Activity Student’s Activity
A. Daily routine
Prayer
Class let’s all stand up.
Before we start, Faye leads the
prayer.
Greetings
Good morning class.
Checking of Attendance
is everybody present for today?
B. Recall
Do you still remember the algebraic
expression?
Great!
A student will lead the prayer.
Dear God… Amen.
Good morning, ma’am.
Yes ma’am, everybody is present today.
Yes ma’am
What is algebraic expression?
Yes, Andrea?
Very good class, now we will
proceed to our lesson. Get your pen
and notebook for our lecture
C. Motivation (G roup work)
Before we start, I will group you
first into four groups. This area will
be the group 1, this area will be the
group 2, this area will be the group
3, and this area will be the group 4.
The name of our activity is WHICH IS
WHICH?
You will determine whether each of the
following is algebraic expression or not.
Polynomial?
- 14x
x
3
√ 2 x + x
- -2014x
x
3
4
1
4
2 x
3
3 x
4
4 x
5
x
3
− 2 x + 1
- x
− 4 x
− 100
100
- 1 − 16 x
2
8 x
2
Let’s analyzed this!
Why they are not algebraic expression?
In this algebraic expression
2 x
3
3 x
4
4 x
5
the group 1 will explain
how it is not a polynomial expression?
The group 2 will explain this
− 4 x
− 100
100
This is for group 3
x
3
4
1
4
And save the best for last the group 4
It is an expression which is made up of
variables and constants, along with
algebraic expression.
Everyone will get their materials
algebraic expression
not algebraic expression
algebraic expression
not algebraic expression
not algebraic expression
algebraic expression
algebraic expression
not algebraic expression
algebraic expression
algebraic expression
the denominator has a variable.
It has negative exponent
it has fractional exponent
there is variable inside a radical sign
so why is it 1?
Yes Camille?
Very Good!
Sometimes there is a polynomial function
that loses the degree of 2, it's still okay, it's
still a polynomial function again, so that we
can write in standard form, our exponent
must be in decreasing order. so always look
at the variable in the variable we're looking
at, okay? not in the coefficient, if you look
at our coefficient the first one is 5. no that's
wrong.
The group 2 will discuss the next thing that
we need to remember to identify if it is a
polynomial and not.
Very Good, group 2.
So, lets have some example.
Decreasing powers of x , the
polynomial function is in standard
form.
the exponent must be arranged in decreasing
order, so that means we always have to look
at the variable. Our variable x must be the
highest exponent to lowest.
here, our highest exponent is 3, so it is the
first one, next is 2 and 1 lastly is the
constant term,
Because we don’t write if the exponent is 1.
The variable has NO/NOT
- negative exponent - fractional exponent
- inside the radical sign
- in the denominator
and then we can call it a polynomial
function when there is no negative
exponent, so our exponent should only be a
whole number. and then there is no fraction
exponent, and also our variable must not be
inside the radical sign, and then there must
be no variable in the denominator.
If you don't see it, it means they are
polynomial function, always remember this
because this is where we can identify if it's a
polynomial function or not.
Example 1: write the given polynomial
functions in standard form.
a) f
x
= 4 x
3
− 16 x − 4 + x
4
− x
2
We need to arrange it in decreasing order.
And Jasmin will do that for us, Jasmin
please write the standard form in the black
board.
Thank you.
So, since there is only one variable that we
used as a variable here let's look at x, so
there we can see who has the highest
exponent.
Eirel, how many term do we have?
We have 5 terms
Who should be first in five terms?
Yes, Paula?
Great!
Also, take note of the sign. The sign of each
term must be the same when you form it in
standard form.
So, this is the standard form of our
polynomial function
f
x
= x
4
3
− x
2
− 16 x − 4
b)
y =
x
4
− x
2
5
3
in this class, don't pay attention to the
fraction, even if it's a decimal, that's okay.
don't ignore it, just pay attention to the
exponent of each variable.
Gabriel, can you please arrange it into
decreasing order or in standard form?
Very Good!
c)
P ( x )=( 3 x + 5 ) ( x + 1 )
This example is it in factored form.
How can we get the standard form of this?
f ( x )= x
4
3
− x
2
− 16 x − 4
Ma’am, we have 5 terms.
x
4
, ma’am.
y = 5 x
5
x
4
3
− x
2
How about the leading coefficient? Kiel?
Very Good.
The degree of polynomial function?
Relaijah?
Lastly, what is the constant term? Paulo?
Very Good, class.
E. Generalization
How can we know if it is a polynomial
function?
Group 3?
Very Good!
Another answer from the group 4?
Very Good.
F. Application (group work)
Every group will make 5 Polynomial
Function and identify the leading term,
leading coefficient, degree, and the constant
term of each Polynomial Function.
I will give you 15 minutes to finish.
Are we clear?
Ma’am because leading term is the term
with the highest exponent of the polynomial
function.
The exponent must be arranged in
decreasing order, so that means we always
have to look at the variable. If the
variabiable is X we must look at the highest
exponent to the lowest exponent.
we can call it a polynomial function when
there is no negative exponent, so our
exponent should only be a whole number.
and then there is no fraction exponent, and
also our variable must not be inside the
radical sign, and then there must be no
variable in the denominator.
If you don't see it, it means they are
polynomial function, because this is where
we can identify if it's a polynomial function
or not.
(the students are working with their group
mates)
Yes ma’am.
G. Evaluation
Determine whether each of the following is a polynomial function or not.
a)
y = 14 x
b) y = 5 x
3
− 4 √ 2 x + x
c)
y = x
3
4
1
4
d) y = 1 − 16 x
2
e)
y =
2 x
3
3 x
4
4 x
5
f) y =− 4 x
− 100
100
H. Assignment
Identify the leading term, leading coefficient, degree and the constant term.
POLYNOMIAL FUNCTION
LEADING
TERM
LEADING
COEFFICIENT
DEGREE
CONSTANT
TERM
y = 4 x
2
− 3 x
4
y = 2 x
3
- f
x
= 2 x
3
− 4 + 2 x
2
y = 5 x − 3 x
2
f
x
= 4 x
2
4
Prepared by:
Erlie M. Muldong
Practice Teacher
Noted by:
Mrs. Mila M. Laxamana
Instructor
