DAILY
LESSON
LOG
Annex to DepEd Order 42,
s.2016
School
Grade
TEN (10)
Level:
Learning Area:
MATHEMATICS
Quarter:
3rd Grading
FR. GRATIAN MURRAY, AFSC INTEGRATED SCHOOL
Teacher
Teaching Dates & Time
I. OBJECTIVES
1. Content Standards
2. Performance Standards
3. Learning Competencies
Objectives
BEVERLY N. ALON
February 27-28, 2023
The learner demonstrates understanding of key concepts of
polynomial function.
The learner is able to conduct systematically a mathematical
investigation involving polynomial functions in different fields.
The learner illustrates polynomial functions. (M10AL-IIa-1)
a. Identify polynomial functions.
b. Illustrate polynomial functions.
c. Value accumulated knowledge as means of new
understanding.
Illustrating Polynomial Functions
II. CONTENT
III. LEARNING RESOURCES
A. References
pp. 86-90
1. Teacher’s Guide
pp. 106-108
2. Learner’s Materials
3. Textbook
4. Additional Materials from Learning
Resources (LR) portal
B. Other Learning Resources
IV. PROCEDURES
A. Reviewing previous lesson or
presenting the new lesson
Grade 10 LCTGs by DepEd Cavite Mathematics 2016
Power point presentation, monitor, show me board, laptop
FACT or BLUFF
Write FACT if the expression being shown is a polynomial, otherwise
write BLUFF.
1. 14𝑥
2. 5𝑥 2 − 4√2𝑥 + 𝑥
3. 𝛱
3
1
4. 𝑥 4 + 3𝑥 4 + 7
5. −4𝑥 −100 + 4𝑥 100
B. Establishing a purpose for the
lesson
C. Presenting examples/Instances
of the new lesson
Using the polynomial function
𝑃(𝑥) = 6𝑥 3 + 4𝑥 2 + 6
How many terms are there?
What is the degree of the polynomial?
What is the leading coefficient?
How about the constant term?
Illustrative examples:
a. The polynomial function (𝒙) = 𝟔𝒙𝟑 + 𝟒𝒙𝟐 + 𝟔 has 3 terms. The
highest power of its terms is 3. Therefore the degree of the polynomial
is 3. The leading coefficient is 6 and the constant term is 6.
b. The polynomial function 𝒚 = 𝟓𝒙𝟐 + 𝟐𝒙𝟑 − 𝒙𝟒 + 𝟑 has 4 terms. The
polynomial function can be written in the standard form 𝒚 = −𝒙𝟒 + 𝟐𝒙𝟑
+ 𝟓𝒙𝟐 + 𝟑 .The leading term is −4𝑥4 , and the degree of the polynomial
is 4. The leading coefficient is −4 and the constant term is 3.
c. Polynomials may also be written in factored form and as a product
of irreducible factors, that is a factor can no longer be factored using
coefficients that are real numbers. The function 𝑦 = 𝑥4 + 2𝑥3 − 13𝑥2 −
10𝑥 in factored form is
𝑦 = (𝑥 − 5)(𝑥 + 1)(𝑥 + 2).
D. Discussing new concepts and
practicing new skills # 1
Fix and Move Them, then Fill Me Up
Direction: Consider the given polynomial functions and fill in the table
below.
Standard
Form
Polynomial Function
D
LC
CT
𝑓(𝑥) = 2 − 11𝑥 + 2𝑥 2
2𝑥 3 5
𝑓(𝑥) =
+ + 15𝑥
3
3
𝑓(𝑥) = 𝑥(𝑥 − 3)
𝑓(𝑥) = 𝑥(𝑥 2 − 5)
𝑦 = 3𝑥 3 + 2𝑥 − 𝑥 4
E. Discussing new concepts and
practicing new skills # 2
F. Developing mastery (leads to
Formative Assessment 3)
G. Finding practical application of
concepts and skills in daily living
Analysis:
1. When are functions polynomials?
2. How can we determine the degree of a polynomial function?
3. In a polynomial function, which is the leading coefficient?
Constant term?
Tell whether the following is a polynomial function or not. Give the
degree and the number of terms for polynomial functions.
1. 𝑦 = 3𝑥 2 − 2𝑥 + 4
2. 𝑦 = 5𝑥+3
𝑥+4
3. 𝑦 =
3
4. 𝑦 = (𝑥 − 4)(4𝑥 + 1)
5. 𝑦 = √6𝑥 2 + 1
Use all the numbers in the box once as coefficients or
exponents to form as may polynomial functions of x as you
can. Write your polynomial function in standard form
1 -2
H. Making generalizations and
abstractions about the lesson
√3
5
2
2 −3 3
A polynomial function is a function in the form
𝑷(𝒙) = 𝒂𝒏𝒙𝒏 + 𝒂𝒏−𝟏𝒙𝒏−𝟏 + 𝒂𝒏−𝟐𝒙𝒏−𝟐 + ⋯+ 𝒂𝟏𝒙𝟏 + 𝒂𝟎,
where 𝑛 is a nonnegative integer, n as a positive integer
implies that:
a. n is not negative
b. n is not zero
c. n is not a fraction
d. n is not a radical, and
e. n is not imaginary
𝑎0 , 𝑎1 , … , 𝑎𝑛 are real numbers called coefficients, 𝑎𝑛 𝑥 𝑛 is
the leading term, 𝑎𝑛 is the leading coefficient, and 𝑎0 is
the constant term.
I. Evaluating learning
Direction: Identify the polynomial functions from the given
set of functions. Give your reasons.
1. 𝑓(𝑥) = 2 − 𝑥 + 3𝑥 2 − 4𝑥 4
2. 𝑃(𝑥) = √5𝑥 7 + 2𝑥 3 − 𝑥
3. 𝑦 = (3𝑥 2 + 2𝑥)2
4. 𝑓(𝑥) = √5𝑥 + 3
5. 𝑦 = −4𝑥 2 + 2𝑥 −1
J. Additional activities for
application or remediation
A. Follow Up
A doll company can make a doll at a cost of P35 per doll.
If the selling of the doll is 𝑥 pesos and the number of dolls
sold per month is 500 − 𝑥,
a. Express the monthly profit in pesos as a function of 𝑥.
b. If the selling price of the doll is P85, determine the
monthly profit. Use the result in letter a.
B. Study
The graph of a Polynomial Function, LM pages 108 – 120
Prepared by:
BEVERLY N. ALON
Teacher I
Checked by:
RICARDO CAMINIAN
Head Teacher 1