CLASS NOTES
SUBJECT : MATHEMATICS
CHAPTER :FUNDAMENTAL CONCEPTS AND
OPERATIONS ON ALGEBRAIC EXPRESSION
Contents
FUNDAMENTAL CONCEPTS AND OPERATIONS ON ALGEBRAIC
EXPRESSION
Algebraic Expressions and Polynomials
In previous lessons, we studied the basic concepts of algebra and operations on algebraic
expressions. This note reviews those concepts and provides additional examples.
1. Constants and Variables
• Constant: A symbol√with a fixed value.
Examples: 5, −2, π, 3, 10
• Variable (Literal): A symbol that can take different numerical values.
Example: In the formula for the area of a rectangle, A = l · w, l and w are variables, while
A depends on their values.
2. Algebraic Expression
An algebraic expression is a combination of constants and variables joined by operations of
addition, subtraction, multiplication, or division.
Examples:
3x + 5, 2ab − 7b + 4, −5x2 y + 3xy − 1
Terms: Parts of an expression separated by + or −.
, Types of Algebraic Expressions
• Monomial: Single term (e.g., 7x2 , 3a)
• Binomial: Two terms (e.g., x + 5, 2ab − 3)
• Trinomial: Three terms (e.g., x2 + xy + y2 )
• Multinomial: More than three terms (e.g., x3 + 2x2 y − xy + 7)
3. Factors and Coefficients
• Factor: Quantity multiplied in a term. Example: In −6xy2 , numerical factor = −6, literal
factors = x, y, y2
• Coefficient: Factor of a term that multiplies the remaining part. Example: In −4ab2 ,
numerical coefficient = −4, literal coefficient = ab2
• Constant term: Term with no variables (e.g., 7 in 3x + 7)
• Like terms: Terms with the same variable part (e.g., 3xy and −5xy) Unlike terms: Terms
with different variable parts (e.g., 2x and 3y)
4. Polynomials
A polynomial is an algebraic expression in which the powers of all variables are non-negative
integers.
Polynomial in One Variable
Example:
3x2 − 5x + 7, 4y − 9
Degree: The highest exponent of the variable in the polynomial.
Polynomials in Two or More Variables
An algebraic expression that contains two or more variables is called a polynomial in several
variables if the exponents of all variables in each term are non-negative integers.
Degree of a polynomial: To find the degree of a polynomial in several variables, add
the powers of all variables in each term. The largest sum among these is the degree of the
polynomial.
SUBJECT : MATHEMATICS
CHAPTER :FUNDAMENTAL CONCEPTS AND
OPERATIONS ON ALGEBRAIC EXPRESSION
Contents
FUNDAMENTAL CONCEPTS AND OPERATIONS ON ALGEBRAIC
EXPRESSION
Algebraic Expressions and Polynomials
In previous lessons, we studied the basic concepts of algebra and operations on algebraic
expressions. This note reviews those concepts and provides additional examples.
1. Constants and Variables
• Constant: A symbol√with a fixed value.
Examples: 5, −2, π, 3, 10
• Variable (Literal): A symbol that can take different numerical values.
Example: In the formula for the area of a rectangle, A = l · w, l and w are variables, while
A depends on their values.
2. Algebraic Expression
An algebraic expression is a combination of constants and variables joined by operations of
addition, subtraction, multiplication, or division.
Examples:
3x + 5, 2ab − 7b + 4, −5x2 y + 3xy − 1
Terms: Parts of an expression separated by + or −.
, Types of Algebraic Expressions
• Monomial: Single term (e.g., 7x2 , 3a)
• Binomial: Two terms (e.g., x + 5, 2ab − 3)
• Trinomial: Three terms (e.g., x2 + xy + y2 )
• Multinomial: More than three terms (e.g., x3 + 2x2 y − xy + 7)
3. Factors and Coefficients
• Factor: Quantity multiplied in a term. Example: In −6xy2 , numerical factor = −6, literal
factors = x, y, y2
• Coefficient: Factor of a term that multiplies the remaining part. Example: In −4ab2 ,
numerical coefficient = −4, literal coefficient = ab2
• Constant term: Term with no variables (e.g., 7 in 3x + 7)
• Like terms: Terms with the same variable part (e.g., 3xy and −5xy) Unlike terms: Terms
with different variable parts (e.g., 2x and 3y)
4. Polynomials
A polynomial is an algebraic expression in which the powers of all variables are non-negative
integers.
Polynomial in One Variable
Example:
3x2 − 5x + 7, 4y − 9
Degree: The highest exponent of the variable in the polynomial.
Polynomials in Two or More Variables
An algebraic expression that contains two or more variables is called a polynomial in several
variables if the exponents of all variables in each term are non-negative integers.
Degree of a polynomial: To find the degree of a polynomial in several variables, add
the powers of all variables in each term. The largest sum among these is the degree of the
polynomial.
