Fundamental Concepts of Algebra 2 GEETHA 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 phrases can be expressed in the form of algebraic expressions 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)

Products are the results of multiplication of constants, variables or both 8𝑥𝑦, 3x, 5y Factor: Each constant and each variable multiplied together to form a product is called a factor of that product. Product Factor 8xy 8, x, y 3x 3, x 5y 5, Y Coefficient: Any factor or group of factors of a product is known as the coefficient of the remaining factors. 𝐼𝑛 𝑡ℎ𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 8𝑥𝑦 Factor Coefficient of 8 xy 8𝑥 y 8x 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+ 3𝑥+ 3 𝑦 Term Type of term 5 a constant. z a variable 3x the product of a constant and a variable 3 y the quotient of a constant and a variable

Terms in an algebraic expression can be like or unlike Unlike Terms: The terms that do not have the same literal coefficients are called unlike terms. Like Terms: The terms having the same literal coefficients are called like terms 3𝑥 𝑎𝑛𝑑 7𝑥 Like 6𝑤 𝑎𝑛𝑑 8𝑦 Unlike 5, 89, 𝑎𝑛𝑑 100 Like 5 𝑎𝑛𝑑 8𝑥 Unlike

A polynomial is an algebraic expression with one or more terms Types of Polynomials 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

Degree of a polynomial 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 8× 𝑥 ×𝑥 =8 𝑥 2 In a polynomial of one variable, degree is the greatest of the exponents ( powers) of its various terms For the polynomial 𝟓 + 𝒙 𝟐 +𝟑 𝒙 𝟓 Exponent of the term 𝑥 2 =2 Exponent of the term 3 𝑥 5 =5 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 𝟑𝒙 + 𝒙 𝒚 𝟐 − 𝟕𝒚𝒛 Sum of the powers of the variables in 3𝑥 = 1 Sum of the powers of the variables in 𝑥 𝑦 2 = 1+2 = 3 Sum of the powers of the variables in 7𝑦𝑧 = 1+1 = 2 The degree of the given polynomial is 3