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