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CHAPTER – 2 
POLYNOMIAL EXPRESSIONS 
A polynomial expression S(x) in one variable x is an algebraic expression in x term as 
? ?
12
1 2 0
............
n n n
n n n
S x a x a x a x ax a
??
??
? ? ? ? ? ?
Where 
10
, ,....... ,
nn
a a a a
?
 are constant and real numbers and 
n
a is not equal to zero.
Some Important points to Note: 
Important Concepts on Polynomial: 
1
Page 2


CHAPTER – 2 
POLYNOMIAL EXPRESSIONS 
A polynomial expression S(x) in one variable x is an algebraic expression in x term as 
? ?
12
1 2 0
............
n n n
n n n
S x a x a x a x ax a
??
??
? ? ? ? ? ?
Where 
10
, ,....... ,
nn
a a a a
?
 are constant and real numbers and 
n
a is not equal to zero.
Some Important points to Note: 
Important Concepts on Polynomial: 
1
Geometric Meaning of the Zeroes of the Polynomial: 
Let’s  us assume 
Y= p (x) where p(x) is the polynomial of any form. 
Now we can plot the equation y=p(x) on the Cartesian plane by taking various values of x 
and y obtained by purring the values. The plot or graph obtained can be of any shapes. 
The zeroes of the polynomial are the points where the graph meet x axis in the Cartesian 
plane. If the graph does not meet x axis, then the polynomial does not have any zero’s. 
Let us take some useful polynomial and shapes obtained on the Cartesian plane 
2
Page 3


CHAPTER – 2 
POLYNOMIAL EXPRESSIONS 
A polynomial expression S(x) in one variable x is an algebraic expression in x term as 
? ?
12
1 2 0
............
n n n
n n n
S x a x a x a x ax a
??
??
? ? ? ? ? ?
Where 
10
, ,....... ,
nn
a a a a
?
 are constant and real numbers and 
n
a is not equal to zero.
Some Important points to Note: 
Important Concepts on Polynomial: 
1
Geometric Meaning of the Zeroes of the Polynomial: 
Let’s  us assume 
Y= p (x) where p(x) is the polynomial of any form. 
Now we can plot the equation y=p(x) on the Cartesian plane by taking various values of x 
and y obtained by purring the values. The plot or graph obtained can be of any shapes. 
The zeroes of the polynomial are the points where the graph meet x axis in the Cartesian 
plane. If the graph does not meet x axis, then the polynomial does not have any zero’s. 
Let us take some useful polynomial and shapes obtained on the Cartesian plane 
2 3
Page 4


CHAPTER – 2 
POLYNOMIAL EXPRESSIONS 
A polynomial expression S(x) in one variable x is an algebraic expression in x term as 
? ?
12
1 2 0
............
n n n
n n n
S x a x a x a x ax a
??
??
? ? ? ? ? ?
Where 
10
, ,....... ,
nn
a a a a
?
 are constant and real numbers and 
n
a is not equal to zero.
Some Important points to Note: 
Important Concepts on Polynomial: 
1
Geometric Meaning of the Zeroes of the Polynomial: 
Let’s  us assume 
Y= p (x) where p(x) is the polynomial of any form. 
Now we can plot the equation y=p(x) on the Cartesian plane by taking various values of x 
and y obtained by purring the values. The plot or graph obtained can be of any shapes. 
The zeroes of the polynomial are the points where the graph meet x axis in the Cartesian 
plane. If the graph does not meet x axis, then the polynomial does not have any zero’s. 
Let us take some useful polynomial and shapes obtained on the Cartesian plane 
2 3
Relation between coefficient and zeros of the polynomial: 
Formation of polynomial when the zeroes are given: 
4
Page 5


CHAPTER – 2 
POLYNOMIAL EXPRESSIONS 
A polynomial expression S(x) in one variable x is an algebraic expression in x term as 
? ?
12
1 2 0
............
n n n
n n n
S x a x a x a x ax a
??
??
? ? ? ? ? ?
Where 
10
, ,....... ,
nn
a a a a
?
 are constant and real numbers and 
n
a is not equal to zero.
Some Important points to Note: 
Important Concepts on Polynomial: 
1
Geometric Meaning of the Zeroes of the Polynomial: 
Let’s  us assume 
Y= p (x) where p(x) is the polynomial of any form. 
Now we can plot the equation y=p(x) on the Cartesian plane by taking various values of x 
and y obtained by purring the values. The plot or graph obtained can be of any shapes. 
The zeroes of the polynomial are the points where the graph meet x axis in the Cartesian 
plane. If the graph does not meet x axis, then the polynomial does not have any zero’s. 
Let us take some useful polynomial and shapes obtained on the Cartesian plane 
2 3
Relation between coefficient and zeros of the polynomial: 
Formation of polynomial when the zeroes are given: 
4
Division algorithm for polynomial: 
Let’s p(x) and q(x) are any two polynomial with q(x) ?0, then we can find polynomial s(x) 
and r(x) such that 
P(x) = s(x) q(x) + r(x) 
Where r(x) can be zero or degree of r(x) < degree of g(x) 
  Dividend = Quotient ? Divisor + Remainder 
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FAQs on Formula Sheet: Polynomials - The Complete SAT Course - Class 10

1. What is a polynomial?
Ans. A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication operations. It can have one or more terms, and the degree of a polynomial is determined by the highest exponent of the variable.
2. How do you classify polynomials based on the number of terms?
Ans. Polynomials can be classified based on the number of terms they have. A polynomial with one term is called a monomial, two terms is called a binomial, and three terms is called a trinomial. Polynomials with more than three terms are generally referred to as polynomials.
3. What is the degree of a polynomial?
Ans. The degree of a polynomial is determined by the highest exponent of the variable in the polynomial. For example, if the highest exponent is 2, the polynomial is of degree 2. The degree helps determine the behavior and properties of the polynomial.
4. How do you perform polynomial addition and subtraction?
Ans. To add or subtract polynomials, you combine like terms. Like terms are terms that have the same variable(s) with the same exponent(s). Simply add or subtract the coefficients of the like terms while keeping the same variables and exponents.
5. Can a polynomial have a negative exponent?
Ans. No, a polynomial cannot have a negative exponent. The exponents in a polynomial must be non-negative integers. Negative exponents are not allowed in polynomials as they would result in fractional or irrational terms, which do not fit the definition of a polynomial.
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