fundamental concepts of algebra geetha venkataraman
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Fundamental Concepts of AlgebraGEETHA VENKATARAMAN
Algebraic expressions are composed of variables and constants• Variables: The letters used
in algebra are called variables or literal numbers or simply literals. They do not have a fixed value.
• Constant: A symbol with a fixed numerical value in all situations is called a constant.
x + 2
Verbal Phrase Algebraic Expression
The sum of six and a number 6 + x
Eight more than a number y + 8
A number plus six n + 6
A number increased by seven x + 7
A number decreased by five n – 5
Ten times a number 10.n or (10n)
Verbal phrases can be expressed in the form of algebraic expressions
Products are the results of multiplication of constants, variables or both
• Factor: Each constant and each variable multiplied together to form a product is called a factor of that product.
8 𝑥𝑦 ,3 x ,5 y
Product Factor8, x, y3, x5, Y
Factor Coefficient of xy8 y8x
• Coefficient: Any factor or group of factors of a product is known as the coefficient of the remaining factors.
Numerical Coefficient:If factor is a
numerical quantity
A term is a constant or a variable or a product or a quotient of constants and variables.
5+𝑧+3 𝑥+3𝑦
Term Type of term a constant.
a variable
the product of a constant and a variable
the quotient of a constant and a variable
Terms in an algebraic expression can be like or unlike• Like Terms: The terms having
the same literal coefficients are called like terms
• Unlike Terms: The terms that do not have the same literal coefficients are called unlike terms.
3 𝑥𝑎𝑛𝑑7 𝑥
6𝑤𝑎𝑛𝑑 8 𝑦
5 ,89 ,𝑎𝑛𝑑100
5𝑎𝑛𝑑 8𝑥
Like
Unlike
Like
Unlike
A polynomial is an algebraic expression with one or more terms
• Monomial: An algebraic expression containing only one term • Example : 3x, 4z, 2y, 5t
• Multinomial: An algebraic expression containing more than one term• Binomial: An algebraic expression containing two terms
• Example: 3y + 5x, 4z – 6y, 2x + 6x• Trinomial: An algebraic expression containing three terms
• Example: 3x + 4z – 3n
Types of Polynomials
8×𝑥×𝑥=8 𝑥2
Power or Exponent of a quantity: When a quantity is multiplied by itself a number of times, the product is called a power of that quantity
Degree of a polynomial
• In a polynomial of one variable, degree is the greatest of the exponents ( powers) of its various terms• For the polynomial
• Exponent of the term • Exponent of the term The degree of the given polynomial is 5
• In a polynomial of two or more variables, degree is the greatest of the sum of the powers of all variables used in each term• For the polynomial
• Sum of the powers of the variables in • Sum of the powers of the variables in • Sum of the powers of the variables in The degree of the given polynomial is 3
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