A Detailed Lesson Plan in MATHEMATICS 10
Section: 10-Sincerity
A. Content Standard: Demonstrates understanding of key concepts of polynomial equations
B. Performance Standard: Able to formulate and solve problems involving polynomial equations
C. MELCS: Illustrates Polynomials Equations (M10AL-li-1)
I. Objectives
At the end of the lesson, the students are expected to:
 Illustrate polynomial equations
 Write polynomial equations in general form
 Identify the leading term, leading coefficient, and the degree of the polynomial
equation
II. Subject Matter:
a. Topic: Polynomial Equations
b. Materials: Laptop, LCD Projector, manila paper
c. References: Grade 10: Intermediate Algebra
d. Strategies: 4A’s
e. Approach: Deductive Approach
III. Learning Task
a. Preliminary
1. Prayer
2. Greetings
3. Checking of Attendance
b. Review/Motivation
Good afternoon, class!
Good afternoon sir!
A. Activity
Tell me who I am.
This morning we will be having an activity called
“Tell me who I am”
Now, what are we going to do if there’s an
activity?
What you are going to do is to guess what the
does pictures says. Do you follow?
B. Analysis
How do you find the activity? Did you enjoy the
activity?
What are your insights about the activity?
What do you think is a polynomial?
That’s a good explanation! Thank You.
1. Cooperate in the activity silently.
2. Avoid loitering.
3. Avoid chatting.
Yes, sir!
Answers may vary.
Answers may vary.
C. Abstraction
Our activity has something to do with our
discussion today. We are going to talk about
Polynomial Equations.
What is a Polynomial?
A Polynomial expression P(x) is an
expression of the form 𝑨𝒏 𝒙𝒏+
𝑨𝒏−𝟏 𝒙𝒏−𝟏 + 𝑨𝒏−𝟐 𝒙𝒏−𝟐 … + 𝑨𝟏 𝒙 + 𝑨𝟎 ,
𝑨𝒏 ≠0, where n is a nonnegative
integer called the degree of the
polynomial and the coefficients
𝑨𝟎 , 𝑨𝟏 , … , 𝑨𝒏 are real numbers.
1. The variables in the expression have a
whole number power
2. It does not contain fractional exponents
3. It does not have negative exponents
4. It does not contain division by a variable
Examples of Polynomial Expressions:
𝟑𝒙+2
𝒙𝟐 + 𝟐𝒙 − 𝟏
𝟑
𝟐𝒙 + 𝒙𝟐 − 𝟒𝒙 − 𝟑
𝟑𝒙𝟒 − 𝟓𝒙𝟑 + 𝒙𝟐 − 𝒙 + 𝟓
𝟓
𝒙 + 𝟐𝒙𝟒 + 𝟑𝒙𝟑 + 𝟒𝒙𝟐 + 𝟓𝒙 + 𝟔
Examples of a non-polynomial
Expressions:
𝟑𝒙−𝟏 +2
𝒙𝟏/𝟐 + 𝟐
𝟏
𝟐𝒙−𝟑 + 𝒙𝟐 + − 𝟏
𝒙
𝟑
−𝟑
𝟐
− 𝟓𝒙 + 𝒙 − 𝒙 + 𝟐
𝒙𝟒
SOME TERMS TO REMEMBER
TYPES OF POLYNOMIALS
Monomials are polynomials that consist
of only one term.
At the end of the lesson, the students are
expected to:
 Illustrate polynomial equations
 Write polynomial equations in
general form
 Identify the leading term,
leading coefficient, and the
degree of the polynomial
equation
Binomials are polynomials that consist
of two terms
Trinomials are polynomials that consist
of three terms
Polynomials with more than three terms
are simply known as Polynomials
DEGREE OF POLYNOMIALS
Linear Polynomial is an expression with
a degree of one (1)
Quadratic Polynomial is an expression
with a degree of two (2)
Cubic Polynomial is an expression with
a degree of three (3)
Quartic Polynomial is an expression
with a degree of four (4)
Quintic Polynomial is an expression
with a degree of five (5)
Activity #2
The class will be divided into three groups.
.
Complete the table.
(Each Group will be given Manila Paper and a
marker with different given in each group)
Answers may vary.
Checking of Outputs
Now I want you to observe the following given.
𝒙−𝟓=𝟎
(𝒙 − 𝟐)(𝒙 + 𝟒)
𝒙𝟐 + 𝟒𝒙 − 𝟏𝟐
𝒙𝟑 − 𝟏 = 𝟎
𝟑𝒙𝟒 + 𝟐𝒙 + 𝟓 = 𝟐𝒙 − 𝟏
𝟐𝒙𝟐 − 𝟔𝟒
Which of the following are Polynomial
Equations?
Okay thank you students.
POLYNOMIAL EQUATION
A Polynomial equation of degree in one variable
x is an equation that can be written in the form
Answers may vary
𝑨𝒏 𝒙𝒏+ 𝑨𝒏−𝟏 𝒙𝒏−𝟏 + 𝑨𝒏−𝟐 𝒙𝒏−𝟐 … + 𝑨𝟏 𝒙 + 𝑨𝟎 =
𝟎
• Degree is the highest power of the
variable that occurs in the polynomial
equation
• Leading Term is the term with the
highest degree
• Leading Coefficient is the coefficient of
the leading term
• Constant term is a term in the
polynomial equation that does not consist
a variable
Activity #3
With the same groupings,
Arrange the given polynomials and write its
standard form in the column provided. Determine
the degree, leading coefficient and the constant
and write these in the appropriate columns. I will
give you 5 minutes to do the task. (Each group
will be given differentiated given)
Checking of outputs
Generalization
Guide Questions:
Again, what are the different types of
Polynomials?
What is a leading coefficient of a
polynomial?
What is a degree in polynomials?
What do you call a polynomial with 2 as
the degree?
When can we say that a given is a
Polynomial Equation?
Very Good!
Any questions and clarification?
If none please get your notebook and answer this
activity.
D. Assessment
Write PE if the given is a Polynomial Equation
and NPE if it is not. If PE write it in General
form and determine the Degree, Leading
Coefficient and the Constant.
1. 𝑥 2 + 2𝑥 −1 − 5 = 0
2. −4 + 𝑥 3 + 2𝑥 + 3𝑥 2 = 0
1
3. 𝑥 + 4
4. 3𝑥 5 − 4𝑥 2 = 0
5. 3𝑥 + 4𝑥 2 + 𝑥 3 = −2
Assignment
Direction: Search in the internet or any source like books in mathematics about real life problems
involving Polynomial Equations.
Prepared by:
RENZ RODNEY R. GAVINO
Teacher I
Checked by:
ROSALINDA B. CABALTERA
Master Teacher I
Date of Observation: __________________