Derive algebric expression, Types of polynomial, zeros of polynomial

1. Saarthi
Classesएक पथदर्शक

2. Saarthi Classes
Sanjaysir , Karjan (7096179109)
Std –10
MathematicsWhat is polynomial?
How to write Algebric expression? And basic terms
How to denote polynomial?
Types of Polynomials.
How to find out Values of Polynomials.
Zeroes of Polynomials

3. Polynomials
What is polynomial?
How to write Algebric expression? And basic terms
related to it.
How to denote polynomial?
Types of Polynomials.
How to find out Values of Polynomials.
Zeroes of Polynomials
Topics in this Video
Part: 1

4. Polynomials: Polynomials are algebraic
expressions or Equations that
include real numbers and variables
If you bought a pen box contain 12 pens, It cost Rs.120. Find
the price of one Pen also Derive the algebraic expression
Algebric
Expression
Suppose, The Price of one Pen = Rs. “ x ”
The Cost of 12 Pens = Rs. 120
(No.of Pens) X ( Cost of One Pen) = Cost of 12 Pens
𝟏𝟐 𝒙 = 𝟏𝟐𝟎
𝟏𝟐 𝒙 – 𝟏𝟐𝟎 = 𝟎

5. Algebric Expression
(Polynomial)12 x – 120 =
0
Coefficien
t
Variabl
e
Constant
Term
Coefficient:
It is number multiplied with Variable
Variable:
Variable is symbol used to represent unknown
quantity
Constant Term
Constant term has well defined number, which has
fixed value

6. How to denote Polynomial ?
If the variable in a polynomial is ‘ x ’ ,
Polynomial can denote by P(x) or q(x) or r(x).
Eg:
P(x)=5x–6
q(x)=2x²-12x+6
r(x)=2x³+ 12x²+6x+6

7. A).Types of Polynomial : On the basis of Numbers of Terms
1. Monomial: Polynomial has only one term are called
Monomial Eg: P(x)=4x orP(x)=2x²
2. Binomial: Polynomial has two terms are called binomial
Eg: P(x)=5x+5
3. Trinomial: Polynomial has three terms are called trinomial
Eg: P(x)=2x²-12x+6

8. B).Types of Polynomial : On the basis of Degree or greatest
exponents of Polynomials
1. Linear Polynomial: A polynomial of degree or power one(1) is
called linear polynomial. Eg: P(x)=3x+5
2. Quadratic Polynomial: A polynomial of degree or power two(2)
is called quadratic polynomial. Eg: P(x)=2x² -12x+6
3. Cubic Polynomial: A polynomial of degree or power three (3)
is called cubic polynomial. Eg: P(x)=2x³+ 12x²+6x+6

9. Polynomials:
Polynomial is algebraic expression made with
constants, variables and exponents
which are combined using addition,
subtraction and multiplication but not division
Polynomials: Not Polynomials:
P(x)=5x –6
q(x)=2x² -12x+6
r(x)=2x³+ 12x²+6x+6
P(x)=5xyˉ² or 5.x/y²
q(x)=
𝟐
𝒙+𝟐
r(x)= 𝒙 − 𝟐

10. How to find out Values of Polynomials?
To find out the values of polynomial in variable ‘x’.
i.e. P(x) = 2 x² - 2
If ‘k’ is any real number, then the value obtained by
replacing ‘x’ by ‘k’ in P(x) ∴ P(k) = 2 k ² - 2
Find the value of polynomial at x = 1, If P(x) = 3 x² + 4 x + 7
P(x) = 3 x² + 4 x + 7
∴ P(1) = 3 (1)² + 4(1) + 7
∴ P(1) = 3+ 4+ 7
∴ P(1) = 14

11. Zeroes of Polynomials
It is the value variable for which the value polynomial becomes zero.
A real number ‘k’ is said to be zero of polynomial 𝑃 𝑥
If 𝑃 𝑘 = 0
How to find out Zeroes of Polynomials?
It is simply equate the polynomial to zero and find the possible values
of variables. ∴ 𝑃 𝑥 = 0
Find the zero of polynomial 𝑷 𝒙 = 𝟏𝟐𝒙 − 𝟏𝟐
𝑷 𝒙 = 𝟎
∴ 𝟏𝟐𝒙 − 𝟏𝟐 = 𝟎
∴ 𝟏𝟐𝒙 = 𝟏𝟐
∴ 𝒙 =
𝟏𝟐
𝟏𝟐
∴ 𝒙 = 𝟏
Verification:
Substitute 𝒙 = 𝟏 in 𝑷 𝒙
Here, 𝒙 = 𝟏 is zero of polynomial 𝑷 𝒙 = 𝟏𝟐𝒙 − 𝟏𝟐
= 𝟏𝟐 (𝟏) − 𝟏𝟐
= 𝟏𝟐 − 𝟏𝟐
= 𝟎
∴ 𝑷 𝒙 = 𝟎

12. How many Zeroes a Polynomials have?
1.Linear Polynomial: Linear polynomial of degree has one(1) has
one(1) zero. 𝑷( 𝒙) = 𝑎. 𝑥 + 𝑏
2.Quadratic Polynomial: Quadratic polynomial of degree two (2) has
two(2) zeroes. 𝑷 𝒙 = 𝑎. 𝑥2
+ 𝑏. 𝑥 + 𝑐
3.Cubic Polynomial: Cubic polynomial of degree three (3) has three
zeroes. 𝑷 𝒙 = 𝑎. 𝑥3
+ 𝑏. 𝑥2
+ 𝑐. 𝑥 + 𝑑

13. Practice Home work
Download worksheet from link given in Description
1. Worksheet 2.1 : Derive algebric expression.
2. Worksheet 2.2: Types of Polynomials
3. Worksheet 2.3: Find out Values of Polynomials and Zeroes of
Polynomials
Password for open worksheet : sanjaysir

14. Next Video
We will studying following topics
1. Geometrical Meaning of Zeroes of Polynomial
a. Graph of Linear Polynomial
b. Graph of Quadratic Polynomial
c. Graph of Cubic Polynomial