Algebra - Polynomials

Algebra A branch of mathematics characterized by the use of variables and operations relating these variables.   Importance of Algebra Algebra serves as a foundation of various concepts and applications of mathematics.   How can Algebra be used in real life? An engineer uses algebra to solve physical problems such as how to build a bridge or design a house. Businessmen use algebra to calculate costs, revenues, and profits. Bankers use Algebra to calculate interests

Word Problem A Filipino citizen is said to be of legal age when he or she turns 18 years old. Romulo, who is a Filipino, was born  in 2001.​ a. In what year will he be of legal age? Solution: 2001 + 18 = 2019 b. In what year will he be 30 years old? Solution: 2001 + 30 = 2031 c. In what year will he be 65 years old? Solution: 2001 +  65 = 2066   Questions (Word Problem) 2001 + 18 2001 + 30 2001 + 65 a. What is the commonality among the solutions?​ 2001 does not change. b. What is the difference among the solutions? The addend changes depending on the given age.   Constant & Variable A constant represents a fixed value. Any number in an expression is a constant.​ A variable is a symbol used to represent values that can change or vary in an expression Example: 2001 + n Constant = 2001 Variable = n

Everyday Constants and Variables  The electric bill each month - Variable The number of days in a week​ - Constant The number of hours of daylight in a day - Variable

Algebraic Expressions An algebraic expression is a combination of one or more constants, and variables along with at least one mathematical operation. Examples: 70r, 70(r), 3x/2y

Translating English Phrases to Mathematical Symbols Addition: The sum of a number and 2​ (or 2 + x since addition is commutative – can be reversed)​ 2 added to a number​ 2 more than a number​ A number increased by 2​ 2 greater than x​ exceeds x by 2​ total of a number and 2​   can be translated to: x + 2   Subtraction:   the difference of x and 2​ a number x decreased by 2​ x reduced by 2​ x take away 2​ a number x less 2​ 2 subtracted from x​ 2 less than x​   can be translated to: x - 2   Multiplication:   2 times x​ the product of 2 and x​ 2 multiplied by x​ twice x​   can be translated to: 2x   Division: x divided by 2 the quotient of x and 2​ the ratio of x to 2​   can be translated to: x ÷ 2   Exponents:  x raised to 2   can be translated to: x^2   Note: "^" is the symbol for exponents.